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arXiv · 1712.05211

Cauchy problem for the incompressible Navier-Stokes equation with an external force

Di Wu
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Abstract

In this paper we focus on the Cauchy problem for the incompressible Navier-Stokes equation with a rough external force. If the given rough external force is small, we prove the local-in-time existence of this system for any initial data belonging to the critical Besov space $\dot{B}_{p,p}^{-1+\frac{3}{p}}$, where $3<p<\infty$. Moreover, We show the long-time behavior of the priori global solutins constructed by us. Also, we give three kinds of uniqueness results of the forced Navier-Stokes equations.

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Di Wu. 2017-12-14. Cauchy problem for the incompressible Navier-Stokes equation with an external force. https://arxiv.org/abs/1712.05211

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