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Creators/Authors contains: "Zhao, Jiefeng"

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  1. ; (, Journal of Differential Equations)
    Full Text Available 
  2. ; (, International Mathematics Research Notices)
    Abstract The global well-posedness on the 2D resistive MHD equations without kinematic dissipation remains an outstanding open problem. This is a critical problem. Any $L^p$-norm of the vorticity $$\omega $$ with $$1\le p<\infty $$ has been shown to be bounded globally (in time), but whether the $$L^\infty $$-norm of $$\omega $$ is globally bounded remains elusive. The global boundedness of $$\|\omega \|_{L^\infty }$$ yields the resolution of the aforementioned open problem. This paper examines the $$L^\infty $$-norm of $$\omega $$ from a different perspective. We construct a sequence of initial data near a special steady state to show that the $$L^\infty $$-norm of $$\omega $$ is actually mildly ill-posed. 
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  3. ; ; ; (, Journal of Evolution Equations)
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