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Global Existence and Optimal Estimation of the Cauchy Problem to the 3D Fluid Equations

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Abstract

This paper is concerned with the Cauchy problem for a class of 3D fluid equations in an infinite cylinder. Based on \(\textrm{L}^q\) energy decay estimates for the corresponding linear equation searching for Green’s matrix and applying Phragmén–Lindelöf method, a solution space in an infinite cylinder is firstly defined. Then we prove the existence of global solutions and their optimal estimation for the 3D fluid equations with repellent and chemo-attractant. As far as we know, this is the first result about the existence of global solutions and their optimal estimation for the 3D fluid equations with repellent and chemo-attractant towards the nonlinear fluid flows in an infinite cylinder.

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Acknowledgements

The author would like to express his sincere gratitude to the reviewers for their valuable comments and suggestions.

Funding

This work is supported by Research start up fund for high level talents of FuZhou University of International Studies and Trade (FWKQJ202006) and Fujian Science and Technology Program Guiding Project (2022H0026).

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  1. Big Data College, Fuzhou University of International Studies and Trade, Fuzhou, 350202, China

    Wenbing Wu

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  1. Wenbing Wu
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Wu, W. Global Existence and Optimal Estimation of the Cauchy Problem to the 3D Fluid Equations. Appl Math Optim 88, 38 (2023). https://doi.org/10.1007/s00245-023-10017-1

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