On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity

By Taoufik Hmidi, Sahbi Keraani. Advances in Differential Equations, 2007

151 citations recorded by the source corpus.

In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity, for rough initial data.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/395587a063d55ba7dd4b01736fc71d7fce687d91

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In Applied Mathematics

1. Changxing Miao
2. Taoufik Hmidi
3. Marius Paicu
4. Jinkai Li
5. Liutang Xue
6. Frédéric Rousset
7. Sahbi Keraani
8. Edriss S. Titi

In Computational Mechanics

1. Taoufik Hmidi
2. Marius Paicu
3. Sahbi Keraani
4. Jinkai Li
5. Edriss S. Titi
6. Raphaël Danchin
7. Changxing Miao
8. Frédéric Rousset

In Mathematical Physics

1. Changxing Miao
2. Taoufik Hmidi
3. Marius Paicu
4. Jinkai Li
5. Liutang Xue
6. Sahbi Keraani
7. Frédéric Rousset
8. Edriss S. Titi

Citations in the corpus

• On the global well-posedness of the Boussinesq system with zero viscosity (2007, methodology): “This result has been recently improved by Keraani and the author [12] to initial data in Hs ×Hs, with s > 0.”
• On the global well-posedness of a class of Boussinesq–Navier–Stokes systems (2009, background): “Later on, Hmidi and Keraani in [9] showed global well-posedness for less regular data (u, θ) ∈ H × H with s > 0.”
• Continuous data assimilation for the 2D Bénard convection through velocity measurements alone (2014, unknown): “For recent results concerning the two-dimensional Boussinesq equations we refer the reader to [7], [11], [21], [23], [24], [29], and references therein.”
• Global well-posedness for a Boussinesq- Navier-Stokes System with critical dissipation (2009, background): “In this paper, we shall focus on system (1.1) which corresponds to the case where the heat conductivity is neglected and Dv = −|D|.”
• 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].”
• 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].”
• Global Well-Posedness of the 2D Boussinesq Equations with Vertical Dissipation (2015, background): “Some generalizations of the results in [3, 14], toward weakening the assumption on the initial data, were established in Hmidi– Keraani [13] and Danchin–Paicu [10]; in particular, no smoothness assumptions on the initial data are required in [10].”
• 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 well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion (2013, unknown): “Global well-posedness results for somewhat rougher initial data (in Besov spaces) is established in [16].”