Global Leray-Hopf weak solutions of the Navier-Stokes equations with Nonzero time-dependent boundary values

R. Farwig, H. Kozono, H. Sohr

研究成果: Chapter

4 引用 (Scopus)

抜粋

In a bounded smooth domain Ω ⸦ ℝ3 and a time interval [0, T), 0 < T ≤ ∞, consider the instationary Navier-Stokes equations with initial value U0 ∈ L2 σ(Ω) and external force f = divF, F ∈ L2(0, T;L2(Ω)). As is well known there exists at least one weak solution in the sense of J. Leray and E. Hopf with vanishing boundary values satisfying the strong energy inequality. In this paper, we extend the class of global in time Leray-Hopf weak solutions to the case when U|∂Ω= g with non-zero time-dependent boundary values g. Although there is no uniqueness result for these solutions, they satisfy a strong energy inequality and an energy estimate. In particular, the long-time behavior of energies will be analyzed.

元の言語English
ホスト出版物のタイトルProgress in Nonlinear Differential Equations and Their Application
出版者Springer US
ページ211-232
ページ数22
DOI
出版物ステータスPublished - 2011 1 1

出版物シリーズ

名前Progress in Nonlinear Differential Equations and Their Application
80
ISSN(印刷物)1421-1750
ISSN(電子版)2374-0280

    フィンガープリント

ASJC Scopus subject areas

  • Analysis
  • Computational Mechanics
  • Mathematical Physics
  • Control and Optimization
  • Applied Mathematics

これを引用

Farwig, R., Kozono, H., & Sohr, H. (2011). Global Leray-Hopf weak solutions of the Navier-Stokes equations with Nonzero time-dependent boundary values. : Progress in Nonlinear Differential Equations and Their Application (pp. 211-232). (Progress in Nonlinear Differential Equations and Their Application; 巻数 80). Springer US. https://doi.org/10.1007/978-3-0348-0075-4_11