[2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability]

** Date: ** 2018-11-17

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

**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 $C^\infty$.

**VOD : **[VIDEO] [YOUTUBE]

Information Center for Mathematical Sciences KAIST

34141 대전광역시 유성구 대학로 291 (구성동373-1)

한국과학기술원(KAIST) 수리과학정보센터

전화 042-350-8196

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2018. ICMS All Rights Reserved.

34141 대전광역시 유성구 대학로 291 (구성동373-1)

한국과학기술원(KAIST) 수리과학정보센터

전화 042-350-8196

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2018. ICMS All Rights Reserved.