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 $\H{m}$, for $m$ large enough. To do so, we introduce a specific symmetrisation allowing areas of null density. Next, we make estimates in $\H{m}$, 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

EXTERNAL FACTORS THAT WILL DRIVE THE NEXT FARM BILL DEBATE

Farm Bill, Federal Budget Deficit, Congressional Budget Office, Political Stakeholders, House Agriculture Committee, Senate Agriculture Committee, Permanent Legislation, Agricultural and Food Policy, Q18,

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