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Energy equality and uniqueness of weak solutions to MHD equations in L ∞(0,T;L n(Ω))

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Abstract

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L ∞(0,T;L n(Ω)). We prove that if the velocity u belongs to the critical space L ∞(0,T;L n(Ω)), the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Yan Yong

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100037, P. R. China

    Quan Sen Jiu

Authors
  1. Yan Yong
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  2. Quan Sen Jiu
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Correspondence to Yan Yong.

Additional information

The research is partially supported by NSF of China (Grant Nos. 10431060 & 10771177)

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Yong, Y., Jiu, Q.S. Energy equality and uniqueness of weak solutions to MHD equations in L ∞(0,T;L n(Ω)). Acta. Math. Sin.-English Ser. 25, 803–814 (2009). https://doi.org/10.1007/s10114-009-7214-8

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  • DOI: https://doi.org/10.1007/s10114-009-7214-8

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