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A class of large solutions to the 3D incompressible MHD and Euler equations with damping

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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 H s 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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Yi Zhou & Yi Zhu

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  1. Yi Zhou
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  2. Yi Zhu
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Correspondence to Yi Zhou.

Additional information

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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Zhou, Y., Zhu, Y. A class of large solutions to the 3D incompressible MHD and Euler equations with damping. Acta. Math. Sin.-English Ser. 34, 63–78 (2018). https://doi.org/10.1007/s10114-016-6271-z

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  • DOI: https://doi.org/10.1007/s10114-016-6271-z

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