Almost sure existence of global weak solutions for incompressible MHD equations in negative-order Sobolev space

Lihuai Du,Ting Zhang

doi:10.1016/j.jde.2017.03.026

Almost sure existence of global weak solutions for incompressible MHD equations in negative-order Sobolev space

Lihuai Du, Ting Zhang

https://doi.org/10.1016/j.jde.2017.03.026

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Journal: Journal of Differential Equations	Publication Date: Mar 22, 2017
Citations: 4	License type: elsevier-specific: oa user license

Affiliation: Zhejiang University

#Existence Of Global Weak Solutions #Initial Data In Hs + Show 8 more

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Abstract

In this paper we consider the Cauchy problem of the incompressible Magnetohydrodynamics (MHD) equations in the periodic space domain TN, where N≥2. After a suitable randomization to the initial data, we obtain the almost sure existence of global weak solutions with the initial data in Hs(TN), s∈(−1,0). Specially, the global weak solution is unique when N=2.

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