A time-dependent perturbation solution from a steady state for Marangoni problem

Abstract

In this article, based on the T-weakly continuous theory, we prove the existence of global weak solution of the 2D incompressible Marangoni problem, which is modelled by the Boussinesq equations omitting effect of buoyancy. Moreover, we show that such weak solution is unique, and which is a time-dependent perturbation solution from a steady state.

Keywords:

• Marangoni problem
• T-weakly continuous theory
• perturbation
• global weak solution

AMS Subject Classifications:

• 35Q35
• 35A01
• 35A02
• 76B03
• 76D07

Acknowledgements

This work was supported by the NSFC [11401479].

Disclosure statement

No potential conflict of interest was reported by the authors.