Global well-posedness of incompressible inhomogeneous fluid systems with bounded density or non-Lipschitz velocity
Language
en
Article de revue
This item was published in
Archive for Rational Mechanics and Analysis. 2013, vol. 209, n° 2, p. 631-682
Springer Verlag
English Abstract
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 ...Read more >
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 $1Read less <
Origin
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