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 -

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's method using Picard'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.