Global large solutions and incompressible limit for the compressible Navier–Stokes system with capillarity

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Abstract

Consider the Cauchy problem for the barotropic compressible Navier–Stokes–Korteweg equations in the whole space Rd (d≥2), supplemented with large initial velocity v0 and almost constant initial density ϱ0. In the two-dimensional case, the global solutions are shown in the critical Besov spaces framework without any restrictions on the size of the initial velocity, provided that the pressure admits a stability condition and the volume viscosity is sufficiently large. The result still holds for the higher dimensional case d≥3 under the additional assumption that the classical incompressible Navier-Stokes equations, supplemented with the initial velocity as the Helmholtz projection of v0, admits a global strong solution.

Original languageEnglish
Article number126675
JournalJournal of Mathematical Analysis and Applications
Volume518
Issue number1
DOIs
Publication statusPublished - 2023 Feb 1

Keywords

  • Besov spaces
  • Incompressible limit
  • Large solutions
  • Navier–Stokes–Korteweg system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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