Work

Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions

Year: 2025

Type: article

Abstract: We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $ \mathcal{A} $ in a domain $ \Omega $ in $ \mathbb{R}^d $. First, under the assumption that slip matrix $ \mathcal{A} $ is sufficiently smooth, we establish a priori local regularity estimates for solutions near a curved portion of the domain boundary. Second, when $ \mathcal{A} $ is the shape operator, we derive local boundary estimates for the Hessians of the solutions, where the right-hand side does not involve the pressure. Notably, our results are new even if the viscosity coefficients are constant.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025092

Authors: Hongjie Dong, Hyunwoo Kwon

Institution: Brown University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Problems in Regularity Theory of Partial Differential Equations