Global classical solutions for partially dissipative hyperbolic system of balance laws

Details Global classical solutions for partially dissipative hyperbolic system of balance laws Global classical solutions for partially dissipative hyperbolic system of balance laws

2012-02-28

arxiv.org/abs/1202.6098v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.

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