Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws

Jiang Xu*, Shuichi Kawashima

*この研究の対応する著者

研究成果: Article査読

22 被引用数 (Scopus)

抄録

The basic existence theory of Kato and Majda enables us to obtain local-in-time classical solutions to generally quasilinear hyperbolic systems in the framework of Sobolev spaces (in x) with higher regularity. However, it remains a challenging open problem whether classical solutions still preserve well-posedness in the case of critical regularity. This paper is concerned with partially dissipative hyperbolic system of balance laws. Under the entropy dissipative assumption, we establish the local well-posedness and blow-up criterion of classical solutions in the framework of Besov spaces with critical regularity with the aid of the standard iteration argument and Friedrichs' regularization method. Then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner spaces (mixed space-time Besov spaces). This fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well-posedness and stability by assuming at all times the Shizuta-Kawashima algebraic condition. As a direct application, the corresponding well-posedness and stability of classical solutions to the compressible Euler equations with damping are also obtained.

本文言語English
ページ(範囲)513-553
ページ数41
ジャーナルArchive for Rational Mechanics and Analysis
211
2
DOI
出版ステータスPublished - 2014 2
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 数学(その他)
  • 機械工学

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