$L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface
$L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface
We prove the $L_p$-$L_q$ maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of …