On the equations of ideal incompressible magneto-hydrodynamics
A note on the generic solvability of the Navier-Stokes equations
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II
Existence theorems for compressible viscous fluids having zero shear viscosity
On the motion of nonviscous compressible fluids in domains with boundary
On nonviscous compressible fluids in a time-dependent domain
On the evolution equations of viscous gaseous stars
On the stationary motion of compressible viscous fluids
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.
A free boundary problem for compressible viscous fluids.
Nonlinear compressible vortex sheets in two space dimensions
We consider supersonic compressible vortex sheets for the isentropic Euler equations of gas dynamics in two space dimensions. The problem is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary is characteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. Nevertheless, we prove the local existence of such piecewise smooth solutions to the Euler equations. Since the a priori estimates for the linearized...
On 3D slightly compressible Euler equations.
Regularity of weakly well-posed characteristic boundary value problems.
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