The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions to a Two-Dimensional Incompressible Dissipative Quasi-Geostrophic Equation
Year: 2023
Author: Linghai Zhang
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 1 : pp. 146–202
Abstract
We will accomplish the exact limits for all order derivatives of the global weak solutions to a two-dimensional incompressible dissipative quasi-geostrophic equation. We will also establish the improved decay estimates with sharp rates for all order derivatives. We will consider two cases for the initial function and the external force and prove the optimal results for both cases. We will couple together existing ideas (including the Fourier transformation and its properties, Parseval’s identity, iteration technique, Lebesgue’s dominated convergence theorem, Gagliardo-Nirenberg-Sobolev interpolation inequality, squeeze theorem, Cauchy-Schwartz’s inequality, etc) existing results (the existence of global weak solutions, the existence of local smooth solution on $(T, ∞)$ and the elementary decay estimate with a sharp rate) and a few novel ideas to obtain the main results.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2023.146
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 1 : pp. 146–202
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 57
Keywords: Incompressible dissipative quasi-geostrophic equation All order derivatives of global weak solution Primary decay estimates exact limits Improved decay estimates with sharp rates.