ANAP Seminar | Speaker: Dmitry Vorotnikov (CMUC),, Universidade de Coimbra

Venue: Sala de Seminários Ed.6-3.08, Campus de Gualtar, 

Online: Link  

Abstract: 

We identify an abstract structural framework underlying many nonlinear PDEs, including the NLS equation with generic power-law nonlinearity as well as the incompressible Euler system. This structure exhibits similarities to hyperbolic conservation laws. The associated abstract problem admits an “entropy” that is formally conserved. The entropy is determined by a strictly convex function that naturally defines an anisotropic Orlicz space. Within this framework, we introduce a dual matrix-valued variational formulation that is reminiscent of `ballistic’ optimal transport. After establishing several results concerning existence, uniqueness and consistency, as an application, we derive a `Dafermos’ principle’: no subsolution of the (primal) problems that fit into our framework can dissipate the total entropy earlier or faster than the strong solution within the latter’s interval of existence.