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Abstract |
We will discuss some recent developments in the analysis of several longstanding problems involving weak continuity and compactness for fundamental nonlinear partial differential equations in mechanics and geometry. In particular, these problems include the inviscid limit of the compressible Navier-Stokes equations to the Euler equations, the construction of global entropy solutions of spherically symmetric solutions to the multidimensional compressible Euler equations, the construction of stochastic entropy solutions to the isentropic Euler equations with random forcing terms, the sonic-subsonic limit of approximate solutions to multidimensional steady Euler equations, the rigidity of isometric embeddings and weak continuity of the Gauss-Coddazi-Ricci equations. This talk will be based mainly on the joint work correspondingly with F.-M. Huang, M. Perepelitsa, M. Slemrod, D. Wang, and T.-Y. Wang. |
