Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

A Priori Estimates for Lagrangian Mean Curvature Flows

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.

Lagrangian Formulation of a Consistent Relativistic Guiding Center Theory

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

A Shock-patching Code for Ultra-relativistic Fluid Flows

We have developed a one-dimensional code to solve ultra-relativistic hydrodynamic problems, using the Glimm method for an accurate treatment of shocks and contact discontinuities. The implementation of the Glimm method is based on an exact Riemann solver and van der Corput sampling sequence. In order to improve computational efficiency, the Glimm method is replaced by a finite differencing sche...

Uniqueness and a Priori Estimates

Under some conditions on f(u), we show that for small, the only solutions to the following elliptic equation u ? u + f(u) = 0 in ; u > 0 in ; @u @ = 0 on @ are constants, provided that R 3 is convex. The proof only uses integration by parts.