Calder{\'o}n splitting and weak solutions for Navier-Stokes equations with initial data in weighted L p spaces

TL;DR

This paper proves the existence of global weak solutions to the 3D Navier-Stokes equations for initial velocities in weighted Lp spaces, utilizing Calderón splitting and energy estimates.

Contribution

It introduces a novel approach combining Calderón splitting with weighted Lp spaces to establish weak solutions for Navier-Stokes with initial data in these spaces.

Findings

Existence of global weak solutions for initial data in weighted Lp spaces.

Use of Calderón splitting to handle initial data in complex function spaces.

Energy controls established in L2 weighted spaces.

Abstract

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces , using Calder{\'o}n splitting L p $\Phi$$\gamma$ $\subset$ L 2 $\Phi$ 2 + L r (with some r $\in$ (3, +$\infty$)) and energy controls in L 2 $\Phi$ 2 .