SIAM Journal on Mathematical Analysis最新文献_第2页

Higher Regularity for Entropy Solutions of Conservation Laws with Geometrically Constrained Discontinuous Flux 具有几何约束不连续通量的守恒定律熵解的较高正则性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-04 DOI: 10.1137/23m1604199

S. S. Ghoshal, S. Junca, A. Parmar

引用次数: 0

Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics 软物质物理学中具有二次锚定的两相复杂流体的全局解决方案

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-04 DOI: 10.1137/23m1608902

Giulia Bevilacqua, Andrea Giorgini

{"title":"Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics","authors":"Giulia Bevilacqua, Andrea Giorgini","doi":"10.1137/23m1608902","DOIUrl":"https://doi.org/10.1137/23m1608902","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6057-6120, October 2024. <br/> Abstract. We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting of a polar liquid crystal immersed in a Newtonian fluid. Such composite material is a paradigmatic example of complex fluids arising in Soft Matter which exhibits multiscale interplay. Beyond the Ginzburg–Landau and Frank elastic energies for the concentration and the polarization, the free energy of the system is characterized by a quadratic anchoring term which tunes the orientation of the polarization at the interface. This leads to several quasi-linear nonlinear couplings in the resulting system describing the macroscopic dynamics. In this work, we establish the first mathematical results concerning the global dynamics of two-phase complex fluids with interfacial anchoring mechanism. First, we determine a set of sufficient conditions on the parameters of the system and the initial conditions which guarantee the existence of global weak solutions in two and three dimensions. Second, we show that weak solutions are unique and globally regular in the two dimensional case. Finally, we complement our analysis with some numerical simulations to display polarization and interfacial anchoring.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Majda and ZND Models for Detonation: Nonlinear Stability vs. Formation of Singularities 爆炸的 Majda 和 ZND 模型：非线性稳定性与奇点的形成

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-04 DOI: 10.1137/23m1544945

Paul Blochas, Aric Wheeler

{"title":"Majda and ZND Models for Detonation: Nonlinear Stability vs. Formation of Singularities","authors":"Paul Blochas, Aric Wheeler","doi":"10.1137/23m1544945","DOIUrl":"https://doi.org/10.1137/23m1544945","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6137-6191, October 2024. <br/> Abstract. In this paper we explore the boundaries of damping estimates by comparing and contrasting two closely related models of combustion, the Majda and ZND models. We are especially concerned with studying the behavior of perturbations of discontinuous waves. On the one hand, we show that singularities form in the unweighted Lipschitz norm on both sides of the shock for both models, extending classical results of John in [Comm. Pure Appl. Math., 27 (1974), pp. 377–405] and Liu in [J. Differential Equations, 33 (1979), pp. 92–111] to suitable variable coefficient systems This involves adapting John’s argument to perturbations of nonconstant waves instead of perturbations of constants. On the other hand, we show instability in exponentially weighted Sobolev spaces for ZND and stability for the Majda model in similarly weighted spaces. This involves proving high order energy estimates, using convective effects and the partial decay coming from a damping term, while being careful with the boundary terms. We note that the convective effects are the origin of the instability in the weighted norm in the ZND model.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Bayesian Model for Dynamic Mass Reconstruction from PET Listmode Data 从 PET 列表模式数据重建动态质量的贝叶斯模型

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m161923x

Marco Mauritz, Bernhard Schmitzer, Benedikt Wirth

引用次数: 0

Strong Ill-Posedness in [math] of the 2D Boussinesq Equations in Vorticity Form and Application to the 3D Axisymmetric Euler Equations 涡度形式的二维布森斯克方程[math]中的强拙问题及其在三维轴对称欧拉方程中的应用

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m159384x

Roberta Bianchini, Lars Eric Hientzsch, Felice Iandoli

{"title":"Strong Ill-Posedness in [math] of the 2D Boussinesq Equations in Vorticity Form and Application to the 3D Axisymmetric Euler Equations","authors":"Roberta Bianchini, Lars Eric Hientzsch, Felice Iandoli","doi":"10.1137/23m159384x","DOIUrl":"https://doi.org/10.1137/23m159384x","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5915-5968, October 2024. <br/> Abstract. We prove the strong ill-posedness of the two-dimensional Boussinesq system in vorticity form in [math] without boundary, building upon the method that Elgindi and Shikh Khalil [Strong Ill-Posedness in [math] for the Riesz Transform Problem, arXiv:2207.04556v1, 2022] developed for scalar equations. We provide examples of initial data with vorticity and density gradient of small [math] size, for which the horizontal density gradient [math] has a strong [math]-norm inflation in infinitesimal time, while the vorticity and the vertical density gradient remain bounded. Furthermore, exploiting the three-dimensional version of Elgindi’s decomposition of the Biot–Savart law, we apply our method to the three-dimensional axisymmetric Euler equations with swirl and away from the vertical axis, showing that a large class of initial data with vorticity uniformly bounded and small in [math] provides a solution whose gradient of the swirl has a strong [math]-norm inflation in infinitesimal time. The norm inflation is quantified from below by an explicit lower bound which depends on time and the size of the data and is valid for small times.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global in Time Weak Solutions to Singular Three-Dimensional Quasi-Geostrophic Systems 奇异三维准地转系统的时间全局弱解

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1552917

Yiran Hu

引用次数: 0

Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and Their Applications 扩展麦克斯韦类型粘弹性系统的残差估计及其应用

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1592456

Maarten V. de Hoop, Masato Kimura, Ching-Lung Lin, Gen Nakamura

{"title":"Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and Their Applications","authors":"Maarten V. de Hoop, Masato Kimura, Ching-Lung Lin, Gen Nakamura","doi":"10.1137/23m1592456","DOIUrl":"https://doi.org/10.1137/23m1592456","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5782-5806, October 2024. <br/> Abstract. In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent estimates for the system of equations for the anisotropic, extended Maxwell model (EMM) and its marginal model; special attention is paid to the introduction of augmented variables. This leads to the augmented system that will also be referred to as the “original” system. A reduced system is then formed which encodes essentially the EMM; it is a closed system with respect to the particle velocity and the difference between the elastic and viscous strains. Based on resolvent estimates, it is shown that the original and reduced systems generate [math]-groups and the reduced system generates a [math]-semigroup of contraction. Naturally, the EMM can be written in an integro-differential form with a relaxation tensor. However, there is a difference between the original and integro-differential systems, in general, with consequences for whether their solutions generate semigroups or not. Finally, an energy estimate is obtained for the reduced system, and it is proven that its solutions decay exponentially as time tends to infinity. The limiting amplitude principle follows readily from these two results.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rigorous Derivation of Michaelis–Menten Kinetics in the Presence of Slow Diffusion 严格推导存在慢扩散的迈克尔斯-门顿动力学

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1579406

Bao Quoc Tang, Bao-Ngoc Tran

引用次数: 0

Existence and Smoothing Effect of Measure Valued Solution to the Homogeneous Boltzmann Equation with Debye–Yukawa Potential 带德拜-汤川势能的均质玻尔兹曼方程的量值解的存在性和平滑效应

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1562123

Shuaikun Wang, Tong Yang

引用次数: 0

Nonmonotonicity of Principal Eigenvalues in Diffusion Rate for Some Non-Self-Adjoint Operators with Large Advection 一些具有大平流的非自交算子扩散率主特征值的非单调性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI: 10.1137/23m1603947

Shuang Liu

引用次数: 0