It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.
The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.
