On Well-posedness of Weak Solutions

Tai-Ping Liu

Institute of Mathematics

Academia Sinica

liu@math.stanford.edu

    There have been very substantial progresses on non-uniqueness of weak solutions for incompressible Navier-Stokes and Euler equations, and compressible Euler equations. The well-posedness problem is a fundamental problem in the theory of partial differential equations. This talk aims at proposing a different well-posedness theory. We illustrate this new theory with a recent study of the author with Shih-Hsien Yu on compressible Navier-Stokes equations, and also recall the celebrated well-posedness theory for hyperbolic conservation laws. This talk gives concrete meaning to the author's talk in annual differential equations meeting at Chung-San University few years ago on the same topic.