There will be an invited talk.

Title: **Green’s functions and Well-posedness of Compressible Navier-Stokes equation**

Speaker: **Prof. Shih-Hsien Yu** (National University of Singapore)

Time: **2018 November 13th, 4:00pm~5:00pm**

Place: **27-220**

Abstract:

A class of decomposition of Green’s functions for the compressilbe Navier-Stokes linearized around a constant state is introduced. The singular structures of the Green’s functions are developed as essential devices to use the nonlinearity directly to covert the 2nd order quasi-linear PDE into a system of zero-th order integral equation with regular integral kernels. The system of integrable equations allows a wider class of functions such as BV solutions. We have shown global existence and well-posedness of the compressible Navier-Stokes equation for isentropic gas with the gas constant γ∈(0,e) in the Lagrangian coordinate for the class of the BV functions and point wise L∞ around a constant state; and the

underline pointwise structure of the solutions is constructed. It is also shown that for the class of BV solution the solution is at most piecewise C2-solution even though the initial data is piecewise C^infty.