The Navier-Stokes equations: on the existence of a weak solution enjoying the energy equality

Paolo Maremonti

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arXiv · 2209.12439

The Navier-Stokes equations: on the existence of a weak solution enjoying the energy equality

Paolo Maremonti

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Abstract

Under the assumption of an initial datum divergence free and in L2, we prove the existence of a weak solution to the Navier-Stokes initial boundary value problem enjoying the energy equality on (0,t), almost everywhere in t>0, in particular, for all t $\in [\theta, \infty)$, with $\theta := \theta(||v0||2)$. Also, the result allows us to refine some others.

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Paolo Maremonti. 2022-09-26. The Navier-Stokes equations: on the existence of a weak solution enjoying the energy equality. https://arxiv.org/abs/2209.12439

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