On the Global Existence of Classical Solutions for Compressible Magnetohydrodynamic Equations

被引：0
作者：
Yang Liu
机构：
[1] Changchun Normal University,College of Mathematics
[2] Nanjing University,Department of Mathematics
来源：
Mathematical Physics, Analysis and Geometry | 2020年 / 23卷
关键词：
Compressible magnetohydrodynamic equations; Cauchy problem; Global classical solution; Large initial velocity; Vacuum; 35B45; 35Q60; 76N10;
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摘要：
This paper deals with the Cauchy problem of compressible magnetohydrodynamic equations in the whole space ℝ3. We show that if, in addition, the conservation law of the total mass is satisfied (i.e., ρ0 ∈ L1), then the global existence theorem with small density and L3-norm of H0 holds for any γ > 1. It is worth mentioning that the initial velocity can be arbitrarily large and the initial vacuum is allowed. Thus, the result obtained particularly extends the one due to Li et al. (SIAM J. Math. Anal., 45:1356–1387, 2013), where the global well-posedness of classical solutions with small energy was proved.
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[1]  
Fan J(2009)Strong solution to the compressible MHD equations with vacuum Nonlinear Anal. Real World Appl. 10 392-409
[2]  
Yu W(2017)Global existence for a class of large solutions to three-dimensional compressible magnetohydrodynamic equations with vacuum SIAM J. Math. Anal. 49 2409-2441
[3]  
Hong G(2012)Global well-posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible Navier-Stokes equations Comm. Pure Appl. Math. 65 549-585
[4]  
Hou X(2013)Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum SIAM J. Math. Anal. 45 1356-1387
[5]  
Peng H(2015)Global classical solutions of 3D isentropic compressible MHD with general initial data Z Angew Math Phys. 66 1777-1797
[6]  
Zhu C(2015)On strong solutions to the Cauchy problem of the two-dimensional compressible magnetohydrodynamic equations with vacuum Nonlinearity 28 509-530
[7]  
Huang X(2016)Global existence and large-time asymptotic behavior of strong solutions to the compressible magnetohydrodynamic equations with vacuum Indiana Univ. Math J. 65 925-975
[8]  
Li J(1959)On elliptic partial differential equations Ann. Sc. Norm. Super. Pisa 13 115-162
[9]  
Xin Z(2018)Global classical solutions of compressible isentropic Navier-Stokes equations with small density Nonlinear Anal. Real World Appl. 42 53-70
[10]  
Li H(1972)The cauchy problem for composite systems of nonlinear differential equations Mat. Sb. 87 504-528
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