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2020•Journal of Mathematical PhysicsRequires access

Strong solutions to the 2D Cauchy problem of nonhomogeneous magnetohydrodynamic equations with vacuum

Boqiang Lü, Xiang Wang, Xin Zhong

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Abstract

In this paper, we study the strong solutions to the Cauchy problem of nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact support. If both the initial density and the initial magnetic field decay not too slow at infinity, the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution.

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What this paper is about

In this paper, we study the strong solutions to the Cauchy problem of nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact support. If both the initial density and the initial magnetic field decay not too slow at infinity, the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the strong solutions to the Cauchy problem of nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact support. If both the initial density and the initial magnetic field decay not too slow at infinity, the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution.

Key concepts: Magnetohydrodynamic drive, Initial value problem, Magnetohydrodynamics, Cauchy problem, Compressibility, Physics, Infinity, Mathematical analysis

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