29,631 research outputs found
Global smooth solutions of Euler equations for Van der Waals gases
We prove global in time existence of solutions of the Euler compressible
equations for a Van der Waals gas when the density is small enough in ,
for large enough. To do so, we introduce a specific symmetrisation allowing
areas of null density. Next, we make estimates in , using for some terms
the estimates done by M. Grassin, who proved the same theorem in the easier
case of a perfect polytropic gas. We treat the remaining terms separately, due
to their non-linearity
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Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions
We show short time existence and uniqueness of \C^{1,1} solutions to the
mean curvature flow with obstacles, when the obstacles are of class \C^{1,1}.
If the initial interface is a periodic graph we show long time existence of the
evolution and convergence to a minimal constrained hypersurface
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