A priori estimates for fluid interface problems

A Priori Estimates for Fluid Interface Problems

We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in H 3 2 k+1 and the velocity fields in H 3 2 . These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.

Optimal a priori estimates for interface problems

Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates

Abstract. For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations. It is shown that both the a priori and the a posteriori error estimates are robust with respect to the diffusion coefficient, i.e., constants in th...

Some New A Priori Estimates for Second OrderElliptic and Parabolic Interface Problems 1

We present some new a priori estimates of the solutions to the second order elliptic and parabolic interface problems. The novelty of these estimates lies in the explicit appearance of the discontinuous coeecients and the jumps of coeecients across the interface.

Uniform a Priori Estimates for Elliptic and Static Maxwell Interface Problems

We present some new a priori estimates of the solutions to threedimensional elliptic interface problems and static Maxwell interface system with variable coefficients. Different from the classical a priori estimates, the physical coefficients of the interface problems appear in these new estimates explicitly.