Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition

Peng Qu; Yanjin Wang

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arXiv · 1508.02867

Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition

Peng Qu·Yanjin Wang

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Abstract

This paper considers the Cauchy problem for the quasilinear hyperbolic system of balance laws in $\mathbb{R}^d$, $d\ge 2$. The system is partially dissipative in the sense that there is an eigen-family violating the Kawashima condition. By imposing certain supplementary degeneracy conditions with respect to the non-dissipative eigen-family, global unique smooth solutions near constant equilibria are constructed. The proof is based on the introduction of the partially normalized coordinates, a delicate structural analysis, a family of scaled energy estimates with minimum fractional derivative counts and a refined decay estimates of the dissipative components of the solution.

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Peng Qu, Yanjin Wang. 2015-08-12. Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition. https://arxiv.org/abs/1508.02867

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