Preprint 2007-002
The Navier–Stokes equations for the motion of compressible, viscous fluid flows with the no-slip boundary condition
Misha Perepelitsa
Abstract: The Navier–Stokes equations for the motion of compressible, viscous fluids in the half-space R3+ with the no-slip boundary condition are studied. Given a constant equilibrium state (ρ̅, 0), we construct a global in time, regular weak solution, provided that the initial data ρ0, u0 are close to the equilibrium state when measured by the norm
| ρ0 − ρ̅|_{L∞} + |u0|_{H1}
and discontinuities of ρ0 decay near the boundary of the half-space R3+.