@Article{ATA-36-2,
author = {Tuoc, Phan and Yannick, Sire},
title = {On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm  Lebesgue Spaces},
journal = {Analysis in Theory and Applications},
year = {2020},
volume = {36},
number = {2},
pages = {111--127},
abstract = {<p style="text-align: justify;">We establish local and global well-posedness of the 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces. The result demonstrates
the persistence of the anisotropic behavior of the initial data under the evolution of
the 2D dissipative quasi-geostrophic equation. The phenomenon is a priori nontrivial
due to the nonlocal structure of the equation. Our approach is based on Kato&#39;s method
using Picard&#39;s iteration, which can be adapted to the multi-dimensional case and
other nonlinear non-local equations. We develop time decay estimates for solutions of
fractional heat equation in mixed norm Lebesgue spaces that could be useful for other
problems.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-0018},
url = {https://global-sci.com/article/73809/on-well-posedness-of-2d-dissipative-quasi-geostrophic-equation-in-critical-mixed-norm-lebesgue-spaces}
}