Global weak solutions to a quantum kinetic-fluid model with large initial data

被引：1

作者：

Li, Yue ^{[1
]}

Sun, Baoyan ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2023年 / 71卷

基金：

中国国家自然科学基金;

关键词：

Kinetic-fluid model; Quantum Bohm potential; Nonlinear friction force; Density-dependent viscosity; Weak solutions; NAVIER-STOKES EQUATIONS; ASYMPTOTIC ANALYSIS; VLASOV EQUATIONS; EULER; SEDIMENTATION; EXISTENCE; SYSTEM;

D O I：

10.1016/j.nonrwa.2022.103822

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a quantum kinetic-fluid model in one-dimensional torus. This model consists of the Vlasov-Fokker-Planck equation coupled with the compressible quantum Navier-Stokes equations via a nonlinear friction force depends on the density of the fluid. The quantum fluid with degenerate viscosity is assumed to be isentropic (adiabatic coefficient gamma > 1). We establish the global weak solutions to this model with arbitrary large initial data. This is the first result on existence of solutions to kinetic-fluid models with density-dependent friction force and degenerate viscosity.(c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：18

共 32 条

[1] Coupling Euler and Vlasov equations in the context of sprays: The local-in-time, classical solutions
Baranger, C
Desvillettes, L
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2006, 3 (01) : 1 - 26
[2] Baranger Celine, 2005, CEMRACS 2004, P41
[3] Berres S., 2004, Computing and Visualization in Science, V6, P67, DOI 10.1007/s00791-003-0110-3
[4] Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression
Berres, S
Bürger, R
Karlsen, KH
Tory, EM
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 64 (01) : 41 - 80
[5] On some compressible fluid models: Korteweg, lubrication, and shallow water systems
Bresch, D
Desjardins, B
Lin, CK
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (3-4) : 843 - 868
[6] On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids
Bresch, Didier
Desjardins, Benoit
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (01): : 57 - 90
[7] On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models
Bresch, Didier
Desjardins, Benoit
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 86 (04): : 362 - 368
[8] Derivation of viscous correction terms for the isothermal quantum Euler model
Brull, S.
Mehats, F.
[J]. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2010, 90 (03): : 219 - 230
[9] Bürger R, 2000, Z ANGEW MATH MECH, V80, P79
[10] GLOBAL BOUNDED WEAK ENTROPY SOLUTIONS TO THE EULER-VLASOV EQUATIONS IN FLUID-PARTICLE SYSTEM
Cao, Wentao
Jiang, Peng
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (04) : 3958 - 3984

← 1 2 3 4 →