The Exact Limits and Improved Decay Estimates for All Order Derivatives of Global Weak Solutions of Three Incompressible Fluid Dynamics Equations (Journal of Nonlinear Modeling and Analysis, 2024)
First of all, the author accomplishes the exact limits for all orderderivatives of the global weak solutions of the $n$-dimensional incompressiblemagnetohydrodynamics equations, the $n$-dimensional incompressible Navier-Stokes equations and the two-dimensional incompressible dissipative quasi-geostrophic equation. Secondly, by making use of the exact limits, he establishes the improved decay estimates with sharp rates for all order derivatives ofthe global weak solutions, for all sufficiently large $t.$ The author proves theseresults by making use of existing ideas, existing results and several new, novelideas.