Local energy weak solutions for the Navier-Stokes equations in the half-space
Language
en
Article de revue
This item was published in
Communications in Mathematical Physics. 2019, vol. 367, n° 2, p. 517–580
Springer Verlag
English Abstract
The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space R3+. Such solutions are sometimes called Lemari´e-Rieusset solutions in the ...Read more >
The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space R3+. Such solutions are sometimes called Lemari´e-Rieusset solutions in the whole space R3. The main tool in our work is an explicit representation formula for the pressure, which is decomposed into a Helmholtz-Leray part and a harmonic part due to the boundary. We also explain how our result enables to reprove the blow-up of the scale-critical L3(R3+) norm obtained by Barker and Seregin for solutions developing a singularity in finite time.Read less <
ANR Project
Bords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027
Origin
Hal imported