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Volume 5, Issue 4
The Exact Limits and Improved Decay Estimates for All Order Derivatives of Global Weak Solutions of Three Incompressible Fluid Dynamics Equations

Linghai Zhang

DOI: 10.12150/jnma.2023.803

J. Nonl. Mod. Anal., 5 (2023), pp. 803-903.

Published online: 2023-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

First of all, the author accomplishes the exact limits for all order derivatives of the global weak solutions of the $n$-dimensional incompressible magnetohydrodynamics 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 of the global weak solutions, for all sufficiently large $t.$ The author proves these results by making use of existing ideas, existing results and several new, novel ideas.

  • Keywords

Incompressible fluid dynamics equations, global weak solutions, all order derivatives, exact limits, improved decay estimates with sharp rates.

  • AMS Subject Headings

35Q20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-803, author = {Zhang , Linghai}, title = {The Exact Limits and Improved Decay Estimates for All Order Derivatives of Global Weak Solutions of Three Incompressible Fluid Dynamics Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {803--903}, abstract = {

First of all, the author accomplishes the exact limits for all order derivatives of the global weak solutions of the $n$-dimensional incompressible magnetohydrodynamics 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 of the global weak solutions, for all sufficiently large $t.$ The author proves these results by making use of existing ideas, existing results and several new, novel ideas.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.803}, url = {http://global-sci.org/intro/article_detail/jnma/22210.html} }
TY - JOUR T1 - The Exact Limits and Improved Decay Estimates for All Order Derivatives of Global Weak Solutions of Three Incompressible Fluid Dynamics Equations AU - Zhang , Linghai JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 803 EP - 903 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.803 UR - https://global-sci.org/intro/article_detail/jnma/22210.html KW - Incompressible fluid dynamics equations, global weak solutions, all order derivatives, exact limits, improved decay estimates with sharp rates. AB -

First of all, the author accomplishes the exact limits for all order derivatives of the global weak solutions of the $n$-dimensional incompressible magnetohydrodynamics 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 of the global weak solutions, for all sufficiently large $t.$ The author proves these results by making use of existing ideas, existing results and several new, novel ideas.

Linghai Zhang. (2023). 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. 5 (4). 803-903. doi:10.12150/jnma.2023.803
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