Quarterly of Applied Mathematics最新文献

{"title":"Rigorous derivation of the compressible Navier–Stokes equations from the two-fluid Navier–Stokes–Maxwell equations","authors":"Yi Peng, Huaqiao Wang","doi":"10.1090/qam/1665","DOIUrl":"https://doi.org/10.1090/qam/1665","url":null,"abstract":"In this paper, we rigorously derive the compressible one-fluid Navier–Stokes equations from the scaled compressible two-fluid Navier–Stokes–Maxwell equations under the assumption that the initial data are well prepared. We justify the singular limit by proving the uniform decay of the error system, which is obtained by using the elaborate energy estimates.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136356124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long time gyrokinetic equations","authors":"C. Cheverry, Shahnaz Farhat","doi":"10.1090/qam/1666","DOIUrl":"https://doi.org/10.1090/qam/1666","url":null,"abstract":"The aim of this text is to elucidate the oscillating patterns (see C. Cheverry [Res. Rep. Math. (2018)]) which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency \u0000\u0000 \u0000 \u0000 \u0000 ε\u0000 \u0000 −\u0000 1\u0000 \u0000 \u0000 ≫\u0000 1\u0000 \u0000 varepsilon ^{-1} gg 1\u0000 \u0000\u0000. By exploiting the properties of underlying integrable systems, we can complement the KAM picture (see G. Benettin and P. Sempio [Nonlinearity 7 (1994), pp. 281–303]; M. Braun [SIAM Rev. 23 (1981), pp. 61–93]) and go beyond the classical results about gyrokinetics (see M. Bostan [Multiscale Model. Simul. 8 (2010), pp. 1923–1957]; A. J. Brizard and T. S. Hahm [Rev. Modern Phys. 79 (2007), pp. 421–468]). The purely magnetic situation was addressed by C. Cheverry [Comm. Math. Phys. 338 (2015), pp. 641–703; J. Differential Equations 262 (2017), pp. 2987–3033]. We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48458067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface for the second special issue in honor of C. M. Dafermos","authors":"Govind Menon","doi":"10.1090/qam/1671","DOIUrl":"https://doi.org/10.1090/qam/1671","url":null,"abstract":"","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43616810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of standing waves for a generalized Benney-Roskes system","authors":"Jose R. Quintero","doi":"10.1090/qam/1654","DOIUrl":"https://doi.org/10.1090/qam/1654","url":null,"abstract":"We analyze the orbital stability of standing waves for a generalized Benney-Roskes system in spatial dimensions \u0000\u0000 \u0000 \u0000 N\u0000 =\u0000 2\u0000 \u0000 N=2\u0000 \u0000\u0000, \u0000\u0000 \u0000 3\u0000 3\u0000 \u0000\u0000. We establish stability of standing waves under certain conditions by reducing the system to a single nonlinear (nonlocal) Schrödinger equation, using the variational characterization of standing waves and a convexity argument.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47383936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A review of recent applications of the relative entropy method to discontinuous solutions of conservation laws","authors":"A. Vasseur","doi":"10.1090/qam/1667","DOIUrl":"https://doi.org/10.1090/qam/1667","url":null,"abstract":"Dafermos [Arch. Rational Mech. Anal. 70 (1979), pp. 167–179] proved the weak/strong principle for conservation laws. It states that Lipschitz solutions to conservation laws endowed with convex entropies are unique and stable among weak solutions. The method, based on relative entropy, was extended by Di Perna [Indiana Univ. Math. J. 28 (1979), pp. 137–188] to show the uniqueness of shocks among weak solutions with strong traces. This theory has been recently revisited with the notion of weighted contractions up to shifts. We review in this paper recent applications of this method, including the weak/BV principle and the stability of discontinuous solutions among inviscid double limits of Navier-Stokes systems.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45905661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"HV geometry for signal comparison","authors":"Ruiyu Han, Dejan Slepvcev, Yunan Yang","doi":"10.1090/qam/1672","DOIUrl":"https://doi.org/10.1090/qam/1672","url":null,"abstract":"In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and vertical deformations. Moreover, it allows for signed signals, which overcomes the main deficiency of optimal transportation-based metrics in signal processing. We characterize the metric properties of the space of signals and establish the regularity and stability of geodesics. Furthermore, we introduce an efficient numerical scheme to compute the geodesics and present several experiments which highlight the nature of the metric.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47887859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a singular Lifshitz-Slyozov-Wagner model","authors":"C. Eichenberg, B. Niethammer, J. Velázquez","doi":"10.1090/qam/1652","DOIUrl":"https://doi.org/10.1090/qam/1652","url":null,"abstract":"<p>We investigate the well-posedness of the classical Lifshitz-Slyozov-Wagner mean-field model for Ostwald ripening with singular coefficients, as they appear, for example in two-dimensional diffusion controlled growth. For Hölder-continuous initial data we prove the existence and uniqueness of a global solution with bounded mean-field. If the data are only in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript l o c Superscript q Baseline left-parenthesis left-bracket 0 comma normal infinity right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msubsup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>l</mml:mi>\u0000 <mml:mi>o</mml:mi>\u0000 <mml:mi>c</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">L^q_{loc}([0,infty ))</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for some <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q greater-than 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">q>1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> we establish global existence of a solution with a mean-field that is in general unbounded but in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript r Baseline left-parenthesis 0 comma upper T right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">L^r(0,T)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for some <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r greater-than 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">r>1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that depends on the coefficients in the model.</p>","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42996868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discretizing advection equations with rough velocity fields on non-Cartesian grids","authors":"Pierre-Emmanuel Jabin, Datong Zhou","doi":"10.1090/qam/1649","DOIUrl":"https://doi.org/10.1090/qam/1649","url":null,"abstract":"We investigate the properties of discretizations of advection equations on non-Cartesian grids and graphs in general. Advection equations discretized on non-Cartesian grids have remained a long-standing challenge as the structure of the grid can lead to strong oscillations in the solution, even for otherwise constant velocity fields. We introduce a new method to track oscillations of the solution for rough velocity fields on any graph. The method in particular highlights some inherent structural conditions on the mesh for propagating regularity on solutions.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136264727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Matrix-scaled resilient consensus of discrete-time and continuous-time networks","authors":"Y. Shang","doi":"10.1090/qam/1662","DOIUrl":"https://doi.org/10.1090/qam/1662","url":null,"abstract":"This paper studies the matrix-scaled resilient consensus problems over multi-agent networks as occurring in computer science and distributed control. Unlike existing works on consensus problems, where the states of agents converge to a common value or reach some prescribed proportions, we take a more general matrix-scaled approach to accommodate the interdependence of multi-dimensional states. We develop a unified analytical framework to deal with matrix-scaled resilient consensus of discrete-time and continuous-time dynamical agents, where the underlying communication network is modeled as a generic directed time-dependent random graph. We propose new distributed protocols to guarantee the matrix-scaled consensus of cooperative agents in the network in the presence of Byzantine agents, who have full knowledge of the system and pose a severe security threat to the collective consensus objective. The cooperative agents feature multiple input and multiple output, and the number and identities of Byzantine agents are not available to the cooperative ones. Our mathematical approach capitalizes on matrix analysis, control theory, graph theory, and martingale convergence. Some numerical examples are presented to demonstrate the effectiveness of our theoretical results.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49657394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Using Bernoulli maps to accelerate mixing of a random walk on the torus","authors":"Gautam Iyer, E. Lu, J. Nolen","doi":"10.1090/qam/1668","DOIUrl":"https://doi.org/10.1090/qam/1668","url":null,"abstract":"<p>We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis 1 slash epsilon squared right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>ε<!-- ε --></mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">O(1/varepsilon ^2)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"epsilon\">\u0000 <mml:semantics>\u0000 <mml:mi>ε<!-- ε --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">varepsilon</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is the step size. Our main results show that for a class of Bernoulli maps, when the random walk is alternated with the Bernoulli map <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi\">\u0000 <mml:semantics>\u0000 <mml:mi>φ<!-- φ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">varphi</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> the mixing time becomes <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis StartAbsoluteValue ln epsilon EndAbsoluteValue right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mi>ln</mml:mi>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mi>ε<!-- ε --></mml:mi>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">O(lvert ln varepsilon rvert )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We also study the <italic>dissipation time</italic> of this process, and obtain <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis StartAbsoluteValue ln epsilon EndAbsoluteValue right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mi>ln</mml:mi>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mi>ε<!-- ε --></mml:mi>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo stretchy=\"false\">)<","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47786720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}