Navier–Stokes equations with external forces in Besov–Morrey spaces

Abstract

In this paper, by adapting the method introduced in H. Kozono and S. Shimizu (Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces. J Funct Anal. 2019;276:896–931), we establish the existence and uniqueness of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov–Morrey space. Also, we show that the local solutions can be extended globally in time provided the initial data and external forces both are small.

Keywords:

• Navier–Stokes equation
• Besov–Morrey space
• maximal Lorentz regularity

2010 Mathematics Subject Classifications:

• 35Q30
• 76D05
• 76D03

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of B.G. is partially supported by the Natural Science Foundation of China [grant 11731014].