AbstractContact structures on 3-manifolds are given by a hyperplane distribution in the tangent bundle satisfying a condition called "complete non-integrability". Contact structures fall into one of two classes: tight or overtwisted. Ozsvath and Szabo introduced invariants of contact structures using Heegaard Floer homology. In this talk, I will survey some recent results about the tightness an...
AbstractIn this talk, we will review the past developments on the solutions of the compressible Navier-Stokes equations and reveal the three hidden structures which linked the weak solution to the strong one. Based on these observations, we proved the Nash's conjecture in 1958s and establish global exsitence theory for both isentropic and heat-conductive compressible Navier-Stokes equations. Mo...