We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to the small viscosity coefficient. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in
L
∞
sense by some compact arguments. Our results show that the transverse magnetic field near the boundary can prevent the strong boundary layers from occurring.
We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to small viscosity coefficients. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in L ∞ sense. It shows that the transverse magnetic field can prevent the boundary layers from occurring in some physical regime.
We establish interior and boundary ε-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations which improve previous results in [18] and [35]. Our proof is based on an iteration argument, Campanato's method, and interpolation techniques.
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