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Unique solvability for the density-dependent Navier–Stokes equations

✍ Scribed by Yonggeun Cho; Hyunseok Kim

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
304 KB
Volume
59
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we consider the incompressible Navier-Stokes equations with a density-dependent viscosity in a bounded domain of R n (n = 2, 3). We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary for a very general initial data. Moreover, we provide a blow-up criterion for the regularity of the strong solution. For these results, the initial density need not be strictly positive. It may vanish in an open subset of .

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✍ Pierre Gilles Lemarié-Rieusset; Ramzi May 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 284 KB

We re-prove various uniqueness theorems for the Navier-Stokes equations, stating the assumptions in terms of multipliers between Sobolev spaces instead of Lebesgue or Lorentz spaces.