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Date | Nov 13, 2018 |
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Speaker | Shih-Hsien Yu |

Dept. | National University of Singapore |

Room | 27-220 |

Time | 16:00-17:00 |

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.

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.

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