On the global well-posedness of the Boussinesq system with zero viscosity
By Taoufik Hmidi, Sahbi Keraani. 2007
159 citations recorded by the source corpus.
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system, with zero viscosity and strictly positive conductivity, for rough initial data.
View Paper: https://www.semanticscholar.org/paper/7e650f6cbefdbe5a83fa3104aee6e2d23e042b28
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- Marius Paicu
- Tarek M. Elgindi
- Raphaël Danchin
- Ping Zhang
- F. Lin
- Xianpeng Hu
- Jingchi Huang
- Taoufik Hmidi
Citations in the corpus
- Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data (2008, result): “This argument provides another proof of Hmidi and Keraani’s result in [13] under somewhat weaker assumptions over θ0 (there having θ0 in (a subspace of) L ∞ was needed).”
- Global Regularity for Some Oldroyd‐B Type Models (2013, background): “A lot of works have been devoted recently to the two-dimensional Boussinesq system with partial dissipation [3], [10], [12], [6] for example.”
- Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1, 2, 3, 11, 12, 15, 16, 24].”
- On a maximum principle and its application to logarithmically critical Boussinesq system (2009, methodology): “This result was improved in [Hmidi and Keraani 2009] to initial data v0 ∈ B (2/p)+1 p,1 and θ0 ∈ B −1+(2/p) p,1 ∩L r , r > 2.”
- GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO (2008, background): “Under various regularity assumptions on the initial data, it has been shown that for arbitrarily large initial data, systems (Bκ,0) with κ > 0 and (B0,ν) with ν > 0 admit a global unique solution (see for example [1, 7, 13, 14, 15, 19, 20]).”
- Global regularity results for the 2D Boussinesq equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1,9,10,12,13, 17,20,22].”