A quasilinear parabolic system with nonlocal boundary condition.
A regularity criterion for the 2D MHD and viscoelastic fluid equations
This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field B, respectively the local deformation gradient F, satisfies for 1/p + 1/q = 1 and 2 < p ≤ ∞, then the corresponding local solution can be extended beyond time T.
A remark on the blowup of solutions to the Laplace equations with nonlinear dynamical boundary conditions.
A smoothing property for the -critical NLS equations and an application to blowup theory