Existence, uniqueness and blow-up of solutions for the 3D Navier–Stokes equations in homogeneous Sobolev–Gevrey spaces

We show existence and uniqueness of solutions for the classical Navier–Stokes equations in Sobolev–Gevrey spaces H ˙ a , σ s ( R 3 ) , where s ∈ ( 1 / 2 , 3 / 2 ) , a > 0 and σ ≥ 1 ; furthermore, we present some blow-up criteria considering these same spaces with σ > 1 .

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Bibliographic Details
Published inComputational & applied mathematics Vol. 39; no. 2
Main Authors Braz e Silva, P., Melo, W. G., Rocha, N. F.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Fluid dynamics
Fluid flow
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Uniqueness
Navier–Stokes equations
Sobolev–Gevrey spaces
35B44
76D03
76D05
35Q30
Blow-up criteria
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Summary:We show existence and uniqueness of solutions for the classical Navier–Stokes equations in Sobolev–Gevrey spaces H ˙ a , σ s ( R 3 ) , where s ∈ ( 1 / 2 , 3 / 2 ) , a > 0 and σ ≥ 1 ; furthermore, we present some blow-up criteria considering these same spaces with σ > 1 .
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-1094-z