811 research outputs found
Two regularity criteria for the 3D MHD equations
This work establishes two regularity criteria for the 3D incompressible MHD
equations. The first one is in terms of the derivative of the velocity field in
one-direction while the second one requires suitable boundedness of the
derivative of the pressure in one-direction
Global Strong solution with vacuum to the 2D nonhomogeneous incompressible MHD system
In this paper, we first prove the unique global strong solution with vacuum
to the two dimensional nonhomogeneous incompressible MHD system, as long as the
initial data satisfies some compatibility condition. As a corollary, the global
existence of strong solution with vacuum to the 2D nonhomogeneous
incompressible Navier-Stokes equations is also established. Our main result
improves all the previous results where the initial density need to be strictly
positive. The key idea is to use some critical Sobolev inequality of
logarithmic type, which is originally due to Brezis-Wainger.Comment: 16 page
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