A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping

Yi ZHOU, Yi ZHU

数学学报(英文) ›› 2018, Vol. 34 ›› Issue (1) : 63-78.

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数学学报(英文) ›› 2018, Vol. 34 ›› Issue (1) : 63-78. DOI: 10.1007/s10114-016-6271-z
Articles

A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping

    Yi ZHOU, Yi ZHU
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A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping

    Yi ZHOU, Yi ZHU
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摘要

In this paper, we derive the global existence of smooth solutions of the 3D incompressible Euler equations with damping for a class of large initial data, whose Sobolev norms Hs can be arbitrarily large for any s ≥ 0. The approach is through studying the quantity representing the difference between the vorticity and velocity. And also, we construct a family of large solutions for MHD equations with damping.

Abstract

In this paper, we derive the global existence of smooth solutions of the 3D incompressible Euler equations with damping for a class of large initial data, whose Sobolev norms Hs can be arbitrarily large for any s ≥ 0. The approach is through studying the quantity representing the difference between the vorticity and velocity. And also, we construct a family of large solutions for MHD equations with damping.

关键词

Large solutions / euler equations / MHD equations / damping

Key words

Large solutions / euler equations / MHD equations / damping

引用本文

导出引用
Yi ZHOU, Yi ZHU. A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping. 数学学报(英文版), 2018, 34(1): 63-78 https://doi.org/10.1007/s10114-016-6271-z
Yi ZHOU, Yi ZHU. A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping. Acta Mathematica Sinica, 2018, 34(1): 63-78 https://doi.org/10.1007/s10114-016-6271-z

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基金

Supported by Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, P. R. China, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, P. R. China, NSFC (Grant No. 11421061), 973 Program (Grant No. 2013CB834100) and 111 project
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