Global well-posedness of incompressible inhomogeneous fluid systems with bounded density or non-Lipschitz velocity
Résumé
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data $a_0\in L^\infty(\R^d)$, $u_0=(u_0^h,u_0^d)\in {\dot B}^{-1+d/p}_{p,r}(\R^d)$, which satisfy $(\mu\|a_0\|_{L^\infty}+\|u_0\|_{{\dot B}^{-1+d/p}_{p,r}})\exp(C_r\mu^{-2r}\|u_0^d\|^{2r}_{{\dot B}^{-1+d/p}_{p,r}} )\leq c_0\mu$ for some positive constants $c_0, C_r$ and $1