Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fluids

Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

We study the isentropic compressible Navier-Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non-negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ0, u0 satisfy the compatibility condition -μΔu0 - (λ + μ) ∇ div u0 + ∇(Aρ0 γ) = ρ0 1/2g for some radially symmetric g ∈ L 2. The initial density ρ0 needs not be positive. We also prove some uniqueness results on the strong solutions.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalMathematical Methods in the Applied Sciences
Volume28
Issue number1
DOIs
Publication statusPublished - 2005 Jan 10

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Radially Symmetric Solutions
Compressible Fluid
Global Existence
Navier Stokes equations
Navier-Stokes Equations
Fluids
Strong Solution
Annular Domains
Global Regularity
Compressible Navier-Stokes Equations
Compatibility Conditions
Weak Solution
Uniqueness
Non-negative

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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