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Global large solutions for the compressible magnetohydrodynamic system

Yanghai Yu|Jinlu Li|Weipeng Zhu
대한수학회 (The Korean Mathematical Society)|2021.11|대한수학회보 (Bulletin of the KMS)|제58권 제6호|pp. 1521-1537|DOI 10.4134/BKMS.b210058

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키워드

Besov spacesCompressible MHD systemglobal solution
주제분류수학

초록

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha \cite{Danchin2017} who considered the compressible Navier-Stokes equations.

Abstract

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha \cite{Danchin2017} who considered the compressible Navier-Stokes equations.

참고문헌 (26)

  1. H. Bahouri, "Fourier analysis and nonlinear partial differential equations" (2011), Springer
  2. H. Cabannes, "Theoretical Magnetohydrodynamics" (1970), Academic Press
  3. Gui-Qiang Chen, "Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data", Journal of Differential Equations, 182(2), pp.344~376 (2002), Elsevier BV[DOI]
  4. Gui-Qiang Chen, "Existence and continuous dependence of large solutions for the magnetohydrodynamic equations", Z. Angew. Math. Phys, 54(4), pp.608~632 (2003), Springer Science and Business Media LLC[DOI]
  5. R. Danchin, "Global existence in critical spaces for compressible Navier-Stokes equations", Inventiones Mathematicae, 141(3), pp.579~614 (2000), Springer Science and Business Media LLC[DOI]
  6. Raphaël Danchin, "LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES", Communications in Partial Differential Equations, 26(7-8), pp.1183~1233 (2001), Informa UK Limited[DOI]
  7. Raphaël Danchin, "Global existence in critical spaces for flows of compressible viscous and heatconductive gases", Archive for Rational Mechanics and Analysis, 160(1), pp.1~39 (2001), Springer Science and Business Media LLC[DOI]
  8. R. Danchin, "Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density", Communications in Partial Differential Equations, 32(9), pp.1373~1397 (2007), Informa UK Limited[DOI]
  9. Raphaël Danchin, "The incompressible limit in Lp type critical spaces", Mathematische Annalen, 366(3-4), pp.1365~1402 (2016), Springer Science and Business Media LLC[DOI]
  10. Raphaël Danchin, "Compressible Navier–Stokes system: Large solutions and incompressible limit", Advances in Mathematics, 320, pp.904~925 (2017), Elsevier BV[DOI]
  11. Bernard Ducomet, "The Equations of Magnetohydrodynamics: On the Interaction Between Matter and Radiation in the Evolution of Gaseous Stars", Communications in Mathematical Physics, 266(3), pp.595~629 (2006), Springer Science and Business Media LLC[DOI]
  12. Jishan Fan, "Vanishing Shear Viscosity Limit in the Magnetohydrodynamic Equations", Communications in Mathematical Physics, 270(3), pp.691~708 (2007), Springer Science and Business Media LLC[DOI]
  13. Jishan Fan, "Global variational solutions to the compressible magnetohydrodynamic equations", Nonlinear Analysis: Theory, Methods & Applications, 69(10), pp.3637~3660 (2008), Elsevier BV[DOI]
  14. Jishan Fan, "Strong solution to the compressible magnetohydrodynamic equations with vacuum", Nonlinear Analysis: Real World Applications, 10(1), pp.392~409 (2009), Elsevier BV[DOI]
  15. Xianpeng Hu, "Global Solutions to the Three-Dimensional Full Compressible Magnetohydrodynamic Flows", Communications in Mathematical Physics, 283(1), pp.255~284 (2008), Springer Science and Business Media LLC[DOI]
  16. Xianpeng Hu, "Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows", Archive for Rational Mechanics and Analysis, 197(1), pp.203~238 (2010), Springer Science and Business Media LLC[DOI]
  17. S. Kawashima, "Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics", Ph.D, pp.1984
  18. L. D. Landau, "Electrodynamics of continuous media" (1960), Pergamon Press
  19. F. Li, "Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces", Kinetic & Related Models, 10(3), pp.741~784 (2017), American Institute of Mathematical Sciences (AIMS)[DOI]
  20. Jinlu Li, "A class large solution of the 3D Hall-magnetohydrodynamic equations", Journal of Differential Equations, 268(10), pp.5811~5822 (2020), Elsevier BV[DOI]
  21. G. Str¨ohmer, "About compressible viscous fluid flow in a bounded region", Pacific J. Math, 143(2), pp.359~375 (1990)[DOI]
  22. Tomio Umeda, "On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics", Japan Journal of Applied Mathematics, 1(2), pp.435~457 (1984), Springer Science and Business Media LLC[DOI]
  23. A. I. Vol’pert, "The Cauchy problem for composite systems of nonlinear differential equations", Mat. Sb. (N. S. ), 87(129), pp.504~528 (1972)
  24. Dehua Wang, "Large Solutions to the Initial-Boundary Value Problem for Planar Magnetohydrodynamics", SIAM Journal on Applied Mathematics, 63(4), pp.1424~1441 (2003), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  25. Xing Wu, "Global existence and asymptotic behavior for the 3D generalized Hall-MHD system", Nonlinear Analysis: Theory, Methods & Applications, 151, pp.41~50 (2017), Elsevier BV[DOI]
  26. J. Zhang, "Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics", Commun. Math. Sci, 8(4), pp.835~850 (2010)[DOI]

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