In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that natural geometric property, associated with reflection symmetries Wulff shape, is preserved flow. Using address and regularity for smooth anisotropies. For non-smooth case establish results types anisotropies known to be globally well-posed.

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid systems, defined whose motion can be expressed the composition two or more Lie-group actions. Hybrid abound fluid dynamics. Examples include: dynamics complex fluids liquid crystals; wind-driven waves propagating with c...

Abstract We study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ n of the mean curvature flow. One our main results is, that complete convex hypersurfaces are products curves and ...