Infinite energy solutions to the Navier-Stokes equations in the\n half-space and applications

2018/03/06 by Christophe Prange, Prange, Christophe
Engineering · Mathematics · #35A01 #35A02 #35B44 #35B45 #35B53 #35C99 #35D30 #35Q30 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1803.02068

openalex publication_date 2018/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This short note serves as an introduction to the papers arXiv:1711.01651 and\narXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the\nexistence of mild solutions on the one hand and local energy weak solutions on\nthe other hand to the Navier-Stokes equations in the half-space R³₊. We\nemphasize a concentration result for (sub)critical norms near a potential\nsingularity. The contents of these notes were presented during the X-EDP\nseminar at IH 'ES in October 2017.\n

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Sur le mouvement d'un liquide visqueux emplissant l'espace

Related

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• Global existence, regularity, and uniqueness of infinite energy\n solutions to the Navier-Stokes equations
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• Rescalings at possible singularities of Navier-Stokes equations in half space
• Infinite energy solutions of the two-dimensional Navier-Stokes equations