TY - JOUR
T1 - On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm  Lebesgue Spaces
AU - Phan , Tuoc
AU - Sire , Yannick
JO - Analysis in Theory and Applications
VL - 2
SP - 111
EP - 127
PY - 2020
DA - 2020/06
SN - 36
DO - http://doi.org/10.4208/ata.OA-0018
UR - https://global-sci.org/intro/article_detail/ata/17111.html
KW - Local well-posedness, global well-posedness, dissipative quasi-geostrophic equation, fractional heat equation, mixed-norm Lebesgue spaces.
AB - <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>