Low regularity global well-posedness for 2D Boussinesq equations with variable viscosity

As a continuation of our previous work, we consider lower regularity global well-posedness for a model of the two-dimensional zero diffusivity Boussinesq equations with variable viscosity. More precisely, based on De Giorgi–Nash–Moser estimates and the refined logarithmic Gronwall-type inequality, w...

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Bibliographic Details
Published in:Journal of mathematical physics 2022-04, Vol.63 (4)
Main Authors: Sun, Weixian, Ye, Zhuan
Format: Article
Language:English
Subjects:
Boussinesq equations
Diffusivity
Physics
Regularity
Two dimensional models
Viscosity
Well posed problems
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Summary:As a continuation of our previous work, we consider lower regularity global well-posedness for a model of the two-dimensional zero diffusivity Boussinesq equations with variable viscosity. More precisely, based on De Giorgi–Nash–Moser estimates and the refined logarithmic Gronwall-type inequality, we prove that it is globally well-posed, provided that the initial data belong to Hs with s > 1. Finally, we show that it is also valid for the two-dimensional zero diffusivity Boussinesq equations with variable viscosity in the non-divergence form.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0082787