- Series
- PDE Seminar
- Time
- Tuesday, February 6, 2024 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Geng Chen – University of Kansas – gengchen@ku.edu – https://people.ku.edu/~g828c364/
- Organizer
- Gong Chen
In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations. The pursuit of solving this intricate problem, particularly concerning singular solutions, persists in both compressible and incompressible scenarios. In particular, compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general.
In this talk, we will discuss the recent proof on the unique vanishing viscosity limit from Navier-Stokes equations to the BV solution of compressible Euler equations, for the general Cauchy Problem. Moreover, we extend our findings by establishing the well-posedness of such solutions within the broader class of inviscid limits of Navier-Stokes equations with locally bounded energy initial values. This is a joint work with Kang and Vasseur, which can be found on arXiv:2401.09305.
The uniqueness and L2 stability of Euler equations, done by Chen-Krupa-Vasseur, will also be discussed in this talk.