Local analyticity radii of solutions to the 3D Navier–Stokes equations with locally analytic forcing

Abstract

We introduce a new method for establishing local analyticity and estimating the local analyticity radius of a solutions to the 3D Navier-Stokes equations at interior points. The approach is based on rephrasing the problem in terms of second order parabolic systems which are then estimated using the mild solution approach. The estimates agree with the global analyticity radius from [16] up to a logarithm.

Local-in-Time Solvability and Space Analyticity for the Navier–Stokes Equations with BMO-Type Initial Data

“…This method was also applied to non-linear heat equations on bounded domains by Grujić and Kukavica [14] for the analyticity at interior points. Later, the technique was refined by Bradshaw et al [6] for local analyticity of the NSE with locally analytic forcing term.…”

Global-in-time Gevrey regularity solution for a class of bistable gradient flows

“…In addition, a few related works for the Cahn-Hilliard model combined with certain fluid motion equation have also been reported, such as [9] for the convective Cahn-Hilliard equation, and [32] for the Cahn-Hilliard-Hele-Shaw model. Other than the Gevrey regularity solutions, a more general class of analytic solutions for different models of incompressible fluid have been discussed in [4,16,22,23,24,25,26,27], etc.…”

“…The analysis of the analytic solution for the NSS model (5.31) will be explored in a future work. The techniques related to the analyticity radius for nonlinear parabolic equations in a bounded domain, as reported by [4,17,22,23,24], are expected to be useful for this work.…”

A direct approach to Gevrey regularity on the half-space

“…This latter fact concerning the analyticity radius which does not vanish as one approaches ∂Ω is the main result of the paper. For a direct method for proving analyticity in the interior, see [1,11].…”