Weak formulation of free-surface wave equations.
Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum
This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the...
Weak solutions for anisotropic nonlinear elliptic equations with variable exponents.
Weakly nonlinear stability analysis of a thin magnetic fluid during spin coating.