@Article{JNMA-5-1,
author = {Zhang, Linghai},
title = {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},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2023},
volume = {5},
number = {1},
pages = {146--202},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2023.146},
url = {https://global-sci.com/article/87865/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}
}