Room 302, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 302室)

Non-existence of Finite Energy Solution to Compressible Navier- Stokes Equations

Hailiang Li (Capital Normal University)

Abstract:

It is an open problem to show the well-posedness of classical solution to compressible Navier-Stokes equations with the density possibly containing vacuum, although the same problem has been proved by Nash and Serrin in energy space in 1960s when the vacuum is excluded. In this talk, we shall prove that there does not exit any classical solution with density being compact supported to the Cauchy problem for one-dimensional compressible Navier- Stokes equations in energy space so long as the initial data satisfy some properties.