With the invitation of Professor Wan-Tong Li of the school of mathematics and statistics of Lanzhou University, Professor Hailiang Li of Capital Normal University, will visit our school from September 14, 2019 to September 17, 2019 to conduct academic exchanges and make an academic report.

Title： Non-existence of finite energy solution to Compressible Navier-Stokes equations

Time：  3:00 p.m.，September 16, 2019

Place： Qiyun building, Room 911

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.

Provincial Key Laboratory of Applied Mathematics and Complex Systems, Gansu Province

Schoolof Mathematicsand Statistics

CuiyingHonorsCollege

September 15, 2019