Global well-posedness for a Boussinesq- Navier-Stokes System with critical dissipation

By Taoufik Hmidi, Sahbi Keraani, Frédéric Rousset. 2009

198 citations recorded by the source corpus.

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e4b605294813131d5cf3bcb51f042a9aeb055cd4

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Nonlinear maximum principles for dissipative linear nonlocal operators and applications (2011, background): “The well-posedness of (B0,2) and (B2,0) have been obtained in [5, 19], while the scaling critical cases (B1,0) and (B0,1) have been resolved in [20] and [21] respectively.”
On the global well-posedness of a class of Boussinesq–Navier–Stokes systems (2009, methodology): “in [12] proved the global result for the rough data through exploiting the new structural properties.”
Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, background): “Further progress on these two cases was recently made by Hmidi, Keraani and Rousset, who were able to establish the global regularity even when the full Laplacian dissipation is replaced by the critical dissipation represented in terms of the operator √ −∆ ([17],[18]).”
Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation (2010, background): “This is discussed in a companion paper [18].”