On initial-boundary value problem of the stochastic Navier–Stokes equations in the half space

Abstract

We study the initial-boundary value problem of the stochastic Navier–Stokes equations in half-space. We prove the existence of weak solutions in standard Besov space-valued random processes when the initial data belong to the critical Besov space.

Keywords:

• Stochastic Navier–Stokes equations
• half space
• existence
• critical Besov space

AMS 2000 subject classifications::

• primary
• 35R60
• secondary
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

T. C. has been supported by the National Research Foundation of Korea No. 2020R1A2C1A01102531. M. Y. has been supported by the National Research Foundation of Korea No. 2021R1A2C4002840, No. 2021K2A9A1A06091213, and by the Yonsei University Research Fund No. 2020-22-0116.