Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum

Huanyuan Li

Applications of Mathematics (2023)

  • Volume: 68, Issue: 5, page 593-621
  • ISSN: 0862-7940

Abstract

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This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the absolute temperature and magnetic field. Then as an immediate application, we prove the global existence and uniqueness of strong solution to the 3D nonhomogeneous heat conducting MHD equations under a smallness condition on the initial data. In addition, the initial vacuum is allowed.

How to cite

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Li, Huanyuan. "Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum." Applications of Mathematics 68.5 (2023): 593-621. <http://eudml.org/doc/299339>.

@article{Li2023,
abstract = {This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the absolute temperature and magnetic field. Then as an immediate application, we prove the global existence and uniqueness of strong solution to the 3D nonhomogeneous heat conducting MHD equations under a smallness condition on the initial data. In addition, the initial vacuum is allowed.},
author = {Li, Huanyuan},
journal = {Applications of Mathematics},
keywords = {heat conducting MHD; Cauchy problem; blowup criterion; global strong solution; vacuum},
language = {eng},
number = {5},
pages = {593-621},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum},
url = {http://eudml.org/doc/299339},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Li, Huanyuan
TI - Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 5
SP - 593
EP - 621
AB - This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the absolute temperature and magnetic field. Then as an immediate application, we prove the global existence and uniqueness of strong solution to the 3D nonhomogeneous heat conducting MHD equations under a smallness condition on the initial data. In addition, the initial vacuum is allowed.
LA - eng
KW - heat conducting MHD; Cauchy problem; blowup criterion; global strong solution; vacuum
UR - http://eudml.org/doc/299339
ER -

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