Uniform regularity of fully compressible Hall-MHD systems
DOI:
https://doi.org/10.58997/ejde.2021.17Keywords:
Hall-MHD; uniform regularity; compressibleAbstract
In this article we study a fully compressible Hall-MHD system. These equations include shear viscosity, bulk viscosity of the flow, and heat conductivity and resistivity coefficients. We prove uniform regularity estimates.
For more information see https://ejde.math.txstate.edu/Volumes/2021/17/abstr.html
References
T. Alazard; Low Mach number limit of the full Navier-Stokes equations, Arch. Ration. Mech. Anal., 180 (2006), 1-73.
W. Cui, Y. Ou, D. Ren; Incompressible limit of full compressible magnetohydrodynamic equations with well-prepared data in 3-D bounded domains. J. Math. Anal. Appl., 427 (2015), 263-288.
C. Dou, S. Jiang, Y. Ou; Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain. J. Differentail Equations, 258 (2015), 379-398.
B. Ducomet, 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.
J. Fan, B. Ahmad, T. Hayat, Y. Zhou; On well-posedness and blow-up for the full compressible Hall-MHD system. Nonlinear Anal. Real World Appl., 31 (2016), 569-579.
J. Fan, B. Alsaedi, T. Hayat, G. Nakamura, Y. Zhou; On strong solutions to the compressible Hall-magnetohydrodynamic system. Nonlinear Anal. Real World Appl., 22 (2015), 423-434.
J. Fan, X. Jia, G. Nakamura, Y. Zhou; On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects. Z. Angew. Math. Phys., 66 (2015), 1695-1706.
J. Fan, W. Yu; Global variational solutionis to the compressible magnetohydrodynamic equations. Nonlinear Anal., 69 (2008), 3637-3660.
J. Fan, W. Yu; Strong solution to the compressible magnetohydrodynamic equations with vacuum. Nonlinear Anal. Real World Appl., 10 (2009), 392-409.
F. He, B. Ahmad, T. Hayat, Y. Zhou; On regularity criteria for the 3D Hall-MHD equations in terms of the velocity. Nonlinear Anal. Real World Appl., 32 (2016), 35-51.
F. He, B. Samet, Y. Zhou; Boundedness and time decay of solutions to a full compressible Hall-MHD system. Bull. Malays. Math. Sci. Soc., 41 (2018), 2151-2162.
X. Hu, D. Wang; Global solutions to the three-demensional full compressible magnetohydro- dynamic flows. Comm. Math. Phys., 283 (2008), 255-284.
X. Hu, 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.
S. Jiang, Q. Ju, F. Li, Z. Xin; Low Mach number limit for the full compressible magnetohy-drodynamic equations with general initial data. Advances in Math., 259 (2014), 384-420.
T. Kato, G. Ponce; Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math., 41 (1988), 891-907.
G. Metivier, S. Schochet; The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal., 158 (2001), 61-90.
D. Shaikh, G. P. Zank; Spectral features of solar wind turbulent plasma. Monthly Notices of the Royal Astronomical Society, 400 (2009), 1881-1891.
H. Triebel; Theory of Function Spaces, in: Monographs in Mathematics, Birkhauser, Verlag, Basel, Boston, 1983.
A. I. Vol'pert, S. I. Hudjaev; The Cauchy problem for composite systems of nonlinear differential equations. Math. USSR. SB., 16 (1972), 504-528.
R. Wan, Y. Zhou; On global existence, energy decay and blow-up criteria for the Hall-MHD system. J. Differential Equations, 259 (2015), 5982-6008.
R. Wan, Y. Zhou; Low regularity well-posedness for the 3D generalized Hall-MHD system. Acta Appl. Math., 147 (2017), 95-111. 10 J. FAN, Y. ZHOU EJDE-2021/17
R. Wan, Y. Zhou; Global well-posedness, BKM blow-up criteria and zero h limit for the 3D incompressible Hall-MHD equations. J. Differential Equations, 267 (2019), 3724-3747.
R. Wan, Y. Zhou; Global well-posedness for the 3D incompressible Hall magnetohydrodynamic equations with Fujita-Kato type initial data. J. Math. Fluid Mech., 21 (2019), Paper No. 5, 16 pp.
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