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On the Global Existence for the Axisymmetric Euler-Boussinesq System in Critical Besov Spaces
- Source :
- Asymptotic Analysis, Asymptotic Analysis, IOS Press, 2012, 77 (1-2), pp.89-121. 〈10.3233/ASY-2011-1074〉, Asymptotic Analysis, IOS Press, 2012, 77 (1-2), pp.89-121. ⟨10.3233/ASY-2011-1074⟩, Asymptotic Analysis, 2012, 77 (1-2), pp.89-121. ⟨10.3233/ASY-2011-1074⟩
- Publication Year :
- 2012
-
Abstract
- This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data $v^{0}{\in}B_{2,1}^{5/2}(\RR^3)$ and$ ${\rho}^{0}{\in}B_{2,1}^{1/2}(\RR^3)\cap L^{p}(\RR^3)$ with $p>6.$ This system couples the incompressible Euler equations with a transport-diffusion equation governing the density. In this case the Beale-Kato-Majda criterion is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity.<br />Comment: Asymptotic Analysis journal, (2011)
- Subjects :
- axisymmetric flows
General Mathematics
010102 general mathematics
Mathematical analysis
Rotational symmetry
Mathematics::Analysis of PDEs
Vorticity
01 natural sciences
global well-posedness
010305 fluids & plasmas
Physics::Fluid Dynamics
symbols.namesake
[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
Mathematics - Analysis of PDEs
critical Besov spaces
0103 physical sciences
FOS: Mathematics
Euler's formula
symbols
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Incompressible euler equations
Uniqueness
0101 mathematics
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 09217134 and 18758576
- Database :
- OpenAIRE
- Journal :
- Asymptotic Analysis, Asymptotic Analysis, IOS Press, 2012, 77 (1-2), pp.89-121. 〈10.3233/ASY-2011-1074〉, Asymptotic Analysis, IOS Press, 2012, 77 (1-2), pp.89-121. ⟨10.3233/ASY-2011-1074⟩, Asymptotic Analysis, 2012, 77 (1-2), pp.89-121. ⟨10.3233/ASY-2011-1074⟩
- Accession number :
- edsair.doi.dedup.....fd65d9a795a07b2f6eb3a6bfb9d5e80a
- Full Text :
- https://doi.org/10.3233/ASY-2011-1074〉