High regularity of solutions of compressible NavierStokes equations
Preprint Series # 776 Cho, Yonggeun High regularity of solutions of compressible NavierStokes equations. (2006); AbstractWe study the NavierStokes equations for compressible {\it
barotropic} fluids in a bounded or unbounded domain $\Omega $ of $
\mathbf{R}^3$. The initial density may vanish in an open subset of
$\Omega$ or to be positive but vanish at space infinity. We first
prove the local existence of solutions $(\rho^{(j)}, u^{(j)})$ in
$C([0,T_* ]; H^{2(kj)+3} \times D_0^1 \cap D^{2(kj)+3} (\Omega )
)$, $0 \le j \le k, k \ge 1$ under the assumptions that the data
satisfy compatibility conditions and that the initial density is
sufficiently small. To control the nonnegativity or decay at
infinity of density, we need to establish a boundary value problem
of $(k+1)$coupled elliptic system which may not be in general
solvable. The smallness condition of initial density is necessary
for the solvability, which is not necessary in case that the
initial density has positive lower bound. Secondly, we prove the
global existence of smooth radial solutions of {\it isentropic}
compressible NavierStokes equations on a bounded annulus or a
domain which is the exterior of a ball under a smallness condition
of initial density. Item Type:  Preprint 

Additional Information:  5 

Uncontrolled Keywords:  viscous compressible
fluids, compressible NavierStokes equations, vacuum 

Subjects:  35xx PARTIAL DIFFERENTIAL EQUATIONS 

ID Code:  1518 

