This note is devoted to some properties of weak solutions to the compressible isentropic Navier-Stokes equations in dimension 2 or 3. First, the restrictions on the pressure growth for the known global existence and stability results are... more
This note is devoted to some properties of weak solutions to the compressible isentropic Navier-Stokes equations in dimension 2 or 3. First, the restrictions on the pressure growth for the known global existence and stability results are illustrated through explicit radial solutions. On the other hand, an improved global time regularity is derived for the momentum.
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation u_tt - c(u)(c(u)u_x)_x=0, for initial data of finite energy. Here c(·) is any smooth function with uniformly... more
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation u_tt - c(u)(c(u)u_x)_x=0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values.
