Free boundary problems for the Navier-Stokes equations

Abstract: The fluid is governed by the Navier-Stokes equations, which are derived from the laws of conservation of momentum and conservation of mass. The Navier-Stokes equations are nonlinear partial differential equations which include the first-order spatial derivative of the velocity vector, called the advection term.

In this talk, we will consider free boundary problems are considered where the boundary of the fluid changes with time, such as raindrops or ocean waves. In particular, I would like to discuss global in time well-posedness of the free boundary problem in an unbounded domain in the scale-invariant space. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space.

Mathematics

Audience: researchers in the discipline

ITB Mathematics Distinguished Lecture Series

Series comments: We aim to bring prominent mathematicians exploring the role of mathematics from various fields, in an intriguing style. The online lectures address quite broad audience, from mathematics students (advanced undergraduate to graduate ones), as well as mathematicians in Indonesia, and our neighboring countries, or even beyond our region. With this lecture series we hope to foster and promote research culture, as well as to highlight the prominent role of mathematics in shaping future society.