Title   name
2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability
  Speaker   Shih-Hsien Yu    
  Date 2018-11-17
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.
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 $gamma in (0,e)$ in the Lagrangian coordinate for the class of the BV functions and point wise $L^infty$ 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 $C^2$-solution even though the initial data is piecewise $C^infty$.