A GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE TWO-DIMENSIONAL VLASOV-FOKKER-PLANCK AND MAGNETOHYDRODYNAMICS EQUATIONS WITH LARGE INITIAL DATA

被引：5

作者：

Huang, Bingkang ^{[1
]}

Zhang, Lan ^{[2
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

基金：

中国国家自然科学基金;

关键词：

Compressible MHD equations; Vlasov-Fokker-Planck equation; global classical solutions; large initial data; vacuum; NAVIER-STOKES EQUATIONS; WELL-POSEDNESS; CAUCHY-PROBLEM; SYSTEM; EULER; INEQUALITIES; EQUILIBRIUM; SPACES; TIME;

D O I：

10.3934/krm.2019016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a two-dimensional coupled system for particles and compressible conducting fluid in an electromagnetic field interactions, which the kinetic Vlasov-Fokker-Planck model for particle part and the isentropic compressible MHD equations for the fluid part, respectively, and these separate systems are coupled with the drag force. For this specific coupled system, a sufficient framework for the global existence of classical solutions with large initial data which may contain vacuum is established.

引用

页码：357 / 396

页数：40

共 38 条

[1]

[Anonymous], 1998, Japan J. Indust. Appl. Math., V15, P51

[2] Global existence of strong solution for the Cucker-Smale-Navier-Stokes system [J].

Bae, Hyeong-Ohk ;

Choi, Young-Pil ;

Ha, Seung-Yeal ;

Kang, Moop-Jin .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (06) :2225-2255

[3] Coupling Euler and Vlasov equations in the context of sprays: The local-in-time, classical solutions [J].

Baranger, C ;

Desvillettes, L .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2006, 3 (01) :1-26

[4]

Baranger C., 2005, CEMRACS 2004 MATH AP, V14, P41

[5] Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression [J].

Berres, S ;

Bürger, R ;

Karlsen, KH ;

Tory, EM .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 64 (01) :41-80

[6]

Boudin L., 2003, Commun. Math. Sci, V1, P657

[7]

Boudin L, 2009, DIFFER INTEGRAL EQU, V22, P1247

[8]

Brezis H., 1980, Comm. Partial Differential Equations, V5, P773

[9]

CAFFARELLI L, 1984, COMPOS MATH, V53, P259

[10] GLOBAL CLASSICAL SOLUTIONS CLOSE TO EQUILIBRIUM TO THE VLASOV-FOKKER-PLANCK-EULER SYSTEM [J].

Carrillo, Jose A. ;

Duan, Renjun ;

Moussa, Ayman .

← 1 2 3 4 →