Quarterly of Applied Mathematics最新文献

{"title":"A causal formulation of dissipative relativistic fluid dynamics with or without diffusion","authors":"H. Freistuhler","doi":"10.1090/qam/1656","DOIUrl":"https://doi.org/10.1090/qam/1656","url":null,"abstract":"The article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second order. The system is determined by four dissipation coefficients \u0000\u0000 \u0000 \u0000 η\u0000 ,\u0000 ζ\u0000 ,\u0000 κ\u0000 ,\u0000 μ\u0000 \u0000 eta ,zeta ,kappa ,mu\u0000 \u0000\u0000, free functions of the fields, which quantify shear viscosity, bulk viscosity, heat conductivity, and diffusion.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45474269","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":"Non-linear singularity formation for circular vortex sheets","authors":"Ryan W. Murray, Galen Wilcox","doi":"10.1090/qam/1659","DOIUrl":"https://doi.org/10.1090/qam/1659","url":null,"abstract":"We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation in two dimensions. In a recent work, the authors demonstrated within this context a marginal linear stability of circular vortex sheets, standing in sharp contrast with classical instability of the flat vortex sheet, which is known as the Kelvin-Helmholtz instability. This article continues that analysis by investigating how non-linear effects induce singularity formation near the circular vortex sheet. In high-frequency regimes, the singularity formation is primarily driven by a complex-valued, conjugated Burgers equation, which we study by modifying a classical argument from hyperbolic conservation laws. This provides a deeper understanding of the mechanisms driving the breakdown of circular vortex sheets, which are observed both numerically and experimentally.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42011968","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":"Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics","authors":"Daria Bolbot, D. Mitsotakis, A. Tzavaras","doi":"10.1090/qam/1658","DOIUrl":"https://doi.org/10.1090/qam/1658","url":null,"abstract":"The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime \u0000\u0000 \u0000 \u0000 ε\u0000 ,\u0000 δ\u0000 →\u0000 0\u0000 \u0000 varepsilon , delta to 0\u0000 \u0000\u0000 with \u0000\u0000 \u0000 \u0000 δ\u0000 =\u0000 o\u0000 (\u0000 ε\u0000 )\u0000 \u0000 delta = o(varepsilon )\u0000 \u0000\u0000, under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44575542","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":"Continua of steadily rotating stars","authors":"W. Strauss","doi":"10.1090/qam/1641","DOIUrl":"https://doi.org/10.1090/qam/1641","url":null,"abstract":"This article is a brief survey of mathematical work, joint with Yilun Wu and Juhi Jang, on models of stars and galaxies. It is a sequel to the survey article by Yilun Wu [Quart. Appl. Math. 78 (2020), pp. 147–159]. The models consider rotating stars (or galaxies or gaseous planets) as composed of particles subject to gravity. Under appropriate conditions, global families of isentropic steadily rotating stars are shown to exist. Local families are also shown to exist even in the presence of variable entropy and arbitrary axisymmetric angular velocity.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49092429","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":"Minimal entropy conditions for scalar conservation laws with general convex fluxes","authors":"G. Cao, Guifang Chen","doi":"10.1090/qam/1669","DOIUrl":"https://doi.org/10.1090/qam/1669","url":null,"abstract":"<p>We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis eta left-parenthesis u right-parenthesis comma q left-parenthesis u right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</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\">(eta (u),q(u))</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"eta left-parenthesis u right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">eta (u)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript normal l normal o normal c Superscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">l</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">o</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">c</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">L^infty _{mathrm { loc}}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that satisfy the inequality: <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"eta left-parenthesis u right-parenthesis Subscript t Baseline plus q left-parenthesis u right-parenthesis Subscript x Baseline less-than-or-equal-to mu\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msu","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43395378","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":"Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics","authors":"D. Serre","doi":"10.1090/qam/1640","DOIUrl":"https://doi.org/10.1090/qam/1640","url":null,"abstract":"We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over \u0000\u0000 \u0000 \u0000 \u0000 \u0000 S\u0000 y\u0000 m\u0000 \u0000 n\u0000 \u0000 (\u0000 \u0000 R\u0000 \u0000 )\u0000 \u0000 mathbf {Sym}_n(mathbb {R})\u0000 \u0000\u0000. This allows us to establish new a priori estimates for inviscid gases flowing in the whole space \u0000\u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 d\u0000 \u0000 mathbb {R}^d\u0000 \u0000\u0000. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47365257","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":"Star dynamics: Collapse vs. expansion","authors":"Mahir Hadžić","doi":"10.1090/qam/1638","DOIUrl":"https://doi.org/10.1090/qam/1638","url":null,"abstract":"We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances and how they interact with nonlinearities to generate imploding finite-time singularities as well as expanding star solutions, arising from smooth initial data. This review paper is based on joint works with Y. Guo, J. Jang, and M. Schrecker.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45524219","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":"Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies","authors":"P. Degond, A. Frouvelle, S. Merino-Aceituno, A. Trescases","doi":"10.1090/qam/1651","DOIUrl":"https://doi.org/10.1090/qam/1651","url":null,"abstract":"We study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44200872","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":"Global stability of almost periodic solutions in population dynamics","authors":"H. Díaz-Marín, O. Osuna","doi":"10.1090/qam/1636","DOIUrl":"https://doi.org/10.1090/qam/1636","url":null,"abstract":"We study first order differential equations with continuous almost periodic time dependence. We propose existence and global stability criteria of almost periodic solutions. Our results are specially useful in the study of one species population dynamics, such as logistic models with almost periodic parameters. Almost periodic time dependence also provides an explanation for oscillatory solutions in models of hematopoiesis disease dynamics.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48019206","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":"Excitation of a layered sphere by 𝑁 acoustic sources: Exact solutions, low-frequency approximations, and inverse problems","authors":"Andreas Kalogeropoulos, N. Tsitsas","doi":"10.1090/qam/1632","DOIUrl":"https://doi.org/10.1090/qam/1632","url":null,"abstract":"Acoustic excitation of a layered sphere by \u0000\u0000 \u0000 N\u0000 N\u0000 \u0000\u0000 external and internal point sources is considered. The direct problem is solved by developing a T-Matrix method leading to the analytical determination of all the involved acoustic fields. Low-frequency far-field approximations are derived for different source distributions and scatterer’s characteristics. The behaviour of the scattering cross sections is investigated. Several inverse problems are formulated and solved analytically; thus the respective unknown quantities are recovered explicitly. These problems include localization of the sources, determination of their number, identification of the core’s type and extraction of the parameters of the scatterer’s layers.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45667259","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}