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- W4289551052 abstract "In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the three-dimensional magneto-hydrodynamic (MHD) system. More precisely, we show that any weak solution $(v,b)in L^p_tL^{infty}_x$ is non-unique in $L^p_tL^{infty}_x$ with $1le p<2$, which reveals the strong non-uniqueness, and the sharpness in terms of the classical Ladyzhenskaya-Prodi-Serrin criteria at endpoint $(2, infty)$. Moreover, for any $1le p<2$ and $epsilon>0$, we construct non-Leray-Hopf weak solutions in $L^p_tL^{infty}_xcap L^1_tC^{1-epsilon}$. The results of Navier-Stokes equations in cite{1Cheskidov} imply the sharp non-uniqueness of MHD system with trivial magnetic field $b$. Our result shows the non-uniqueness for any weak solution $(v,b)$ including non-trivial magnetic field $b$." @default.
- W4289551052 created "2022-08-03" @default.
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- W4289551052 date "2022-07-30" @default.
- W4289551052 modified "2023-10-16" @default.
- W4289551052 title "Sharp and strong non-uniqueness for the magneto-hydrodynamic equations" @default.
- W4289551052 doi "https://doi.org/10.48550/arxiv.2208.00228" @default.
- W4289551052 hasPublicationYear "2022" @default.
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