Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

TL;DR

This paper proves that weak solutions to 2D Navier-Stokes equations with dynamic slip boundary conditions are strong under regular data and provides explicit bounds on the attractor's fractal dimension, aligning with Dirichlet case results.

Contribution

It establishes regularity of solutions and derives explicit bounds on the attractor dimension for 2D NSE with dynamic boundary conditions, extending existing results.

Findings

Weak solutions are shown to be strong with regular data.

Explicit upper bounds for the fractal dimension of the global attractor are provided.

Results are consistent with those for Dirichlet boundary conditions.

Abstract

We consider incompressible Navier-Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.