Glasnik Matematicki, Vol. 57, No. 2 (2022), 281-290. \( \)
UNIFORM REGULARITY FOR THE NONISENTROPIC MHD SYSTEM
Kunlong Shi and Tong Tang
College of Sciences, Nanjing Forestry University, 210037 Nanjing, P.R. China
e-mail:skl@njfu.edu.cn
School of Mathematical Science, Yangzhou University, 225002 Yangzhou, P.R. China
e-mail:tt0507010156@126.com
Abstract.
In this work, we prove the uniform regularity of smooth solutions to the full compressible MHD system in \(\mathbb{T}^3\). Here our result is obtained by using the
bilinear commutator and product estimates.
2020 Mathematics Subject Classification. 35Q30, 35Q35, 76D03
Key words and phrases. MHD, compressible, uniform regularity.
Full text (PDF) (access from subscribing institutions only)
https://doi.org/10.3336/gm.57.2.08
References:
-
T. Alazard, Low Mach number limit of the full Navier-Stokes equations, Arch. Ration. Mech. Anal. 180 (2006), 1–73.
MathSciNet
CrossRef
-
X. Blanc, B. Ducomet and Š. Nečasová, Global existence of a radiative Euler system coupled to an electromagnetic field, Adv. Nonlinear Anal. 8 (2019), 1158–1170.
MathSciNet
CrossRef
-
B. Ducomet and E. Feireisl, The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars, Comm. Math. Phys. 266 (2006), 595–629.
MathSciNet
CrossRef
-
B. Ducomet, M. Kobera and Š. Nečasová, Global existence of a weak solution for a model in radiation magnetohydrodynamics, Acta Appl. Math. 150 (2017), 43–65.
MathSciNet
CrossRef
-
J. Fan and W. Yu, Strong solution to the compressible magnetohydrodynamic equations with vacuum, Nonlinear Anal. Real World Appl. 10 (2009), 392–409.
MathSciNet
CrossRef
-
J. Fan and W. Yu, Global variational solutions to the compressible magnetohydrodynamic equations, Nonlinear Anal. 69 (2008), 3637–3660.
MathSciNet
CrossRef
-
X. Blanc, B. Ducomet and Š. Nečasová, Global existence of a diffusion limit with damping for the compressible radiative Euler system coupled to an electromagnetic field, Topol. Methods Nonlinear Anal. 52 (2018), 285–309.
MathSciNet
CrossRef
-
J. Fan, F. Li, G. Nakamura and Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations, J. Differential Equations 256 (2014), 2858–2875.
MathSciNet
CrossRef
-
D. Hoff and E. Tsyganov, Uniqueness and continuous dependence of weak solutions in compressible magnetohydrodynamics, Z. Angew. Math. Phys. 56 (2005), 791–804.
MathSciNet
CrossRef
-
X. Hu and D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys. 283 (2008), 255–284.
MathSciNet
CrossRef
-
X. Hu and D. Wang, Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows, Arch. Ration. Mech. Anal. 197 (2010), 203–238.
MathSciNet
CrossRef
-
X. Huang and J. Li, Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows, Comm. Math. Phys. 324 (2013), 147–171.
MathSciNet
CrossRef
-
T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), 891–907.
MathSciNet
CrossRef
-
D. Li, On Kato-Ponce and fractional Leibniz, Rev. Mat. Iberoam. 35 (2019), 23–100.
MathSciNet
CrossRef
-
G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal. 158 (2001), 61–90.
MathSciNet
CrossRef
-
A. I. Vol'pert and S. I. Hudjaev, The Cauchy problem for composite systems of nonlinear differential equations, Mat. Sb. (N.S.) 87(129) (1972), 504–528.
MathSciNet
-
Y. Wang, L. Du and S. Li, Blowup mechanism for viscous compressible heat-conductive magnetohydrodynamic flows in three dimensions, Sci. China Math. 58 (2015), 1677–1696.
MathSciNet
CrossRef
-
Y. Wang, A Beale-Kato-Majda criterion for three dimensional compressible viscous non-isentropic magnetohydrodynamic flows without heat-conductivity, J. Differential Equations 280 (2021), 66–98.
MathSciNet
CrossRef
Glasnik Matematicki Home Page