Abstract In this talk we discuss a generalized Lax equivalence theory for the compressible Navier-Stokes system: convergence = stability + consistency. First, we introduce the concept of consistent approximation representing the (energy/entropy) stability and consistency of suitable numerical solutions. Then, by passing to the limit we obtain a dissipative weak solution with the only informatio...
Abstract:The systole of a closed Riemannian manifold is defined to be the length of a shortest noncontractible loop. Gromov's systolic inequality relates systole to volume, which is a curvature free inequality. Gromov proved that systolic inequality holds on closed essential manifolds. Gromov's further work indicates that systolic inequality is related to topological complicatedness of manifol...