Abstract
In this paper we study a transport-diffusion model with some logarithmic dissipations. We look for two kinds of estimates. The first is a maximum principle whose proof is based on Askey theorem concerning characteristic functions and some tools from the theory of -semigroups. The second is a smoothing effect based on some results from harmonic analysis and submarkovian operators. As an application we prove the global well-posedness for the two-dimensional Euler–Boussinesq system where the dissipation occurs only on the temperature equation and has the form , with . This result improves on an earlier critical dissipation condition needed for global well-posedness.
Citation
Taoufik Hmidi. "On a maximum principle and its application to the logarithmically critical Boussinesq system." Anal. PDE 4 (2) 247 - 284, 2011. https://doi.org/10.2140/apde.2011.4.247
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