On the Analyticity of Solutions to the Navier-Stokes Equations with Fractional Dissipation

TL;DR

This paper proves that solutions to the Navier-Stokes equations with fractional dissipation are analytic in space, using new bilinear estimates, pointwise kernel bounds, and fractional bootstrap techniques.

Contribution

Introduces a novel approach combining bilinear estimates, kernel analysis, and fractional bootstrap to establish analyticity of solutions with fractional dissipation.

Findings

Solutions are analytic in space variables.

New bilinear estimate developed for fractional dissipation.

Analyticity proven using fractional bootstrap method.

Abstract

By using a new bilinear estimate, a pointwise estimate of the generalized Oseen kernel and an idea of fractional bootstrap, we show in this note that solutions to the Navier-Stokes equations with fractional dissipation are analytic in space variables.