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arxiv: 1807.07063 · v1 · pith:Y6W7JY4Hnew · submitted 2018-07-18 · 🧮 math.AP

On the explicit blowup solutions for 3D incompressible Magnetohydrodynamics equations

Weiping Yan This is my paper
classification 🧮 math.AP
keywords blowupsolutionsincompressibleequationsexplicitfamilydatafield
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This paper concerns with the explicit blowup phenomenon for 3D incompressible MHD equations in R^3. More precisely, we find two family of explicit blowup solutions for 3D incompressible MHD equations in R^3. One family of solutions admit the smooth initial data, and the initial data of another family of solutions are not smooth. The energy of those solutions is infinite. Moreover, our results tell us that the blowup phenomenon of 3D incompressible MHD can only take place in the velocity field of the fluid, but no blowup for the magnetic field.

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  1. Asymptotic stability of explicite infinite energy blowup solutions for three dimensional incompressible Magnetohydrodynamics equations

    math.AP 2019-07 unverdicted novelty 5.0

    Explicit finite-time blowup solutions for 3D incompressible MHD are constructed with infinite energy and shown to be asymptotically stable in a time-dependent shrinking domain.