Local Energy Weak Solutions for the Navier–Stokes Equations in the Half-Space View Full Text


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Article Info

DATE

2019-04

AUTHORS

Yasunori Maekawa, Hideyuki Miura, Christophe Prange

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 R+3. Such solutions are sometimes called Lemarié–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(R+3) norm obtained by Barker and Seregin for solutions developing a singularity in finite time. More... »

PAGES

1-64

References to SciGraph publications

  • 1934-12. Sur le mouvement d'un liquide visqueux emplissant l'espace in ACTA MATHEMATICA
  • 2001-03. $ L^p $-Theory of the Stokes equation in a half space in JOURNAL OF EVOLUTION EQUATIONS
  • 2015-03. Uniform Boundedness and Long-Time Asymptotics for the Two-Dimensional Navier–Stokes Equations in an Infinite Cylinder in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 2011-06-10. A Note on Necessary Conditions for Blow-up of Energy Solutions to the Navier-Stokes Equations in PARABOLIC PROBLEMS
  • 2012-06. A Certain Necessary Condition of Potential Blow up for Navier-Stokes Equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-08. A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 2002-02. Local Regularity of Suitable Weak Solutions to the Navier—Stokes Equations Near the Boundary in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 2007-03. Navier–Stokes Equations: Almost L3,∞-Case in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 2017-12. A necessary condition of potential blowup for the Navier–Stokes system in half-space in MATHEMATISCHE ANNALEN
  • 2014-03. The L∞-Stokes semigroup in exterior domains in JOURNAL OF EVOLUTION EQUATIONS
  • 2015-09. The Navier–Stokes Equations in a Space of Bounded Functions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-09. Backward Uniqueness for Parabolic Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2014-04. Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions in INVENTIONES MATHEMATICAE
  • 2013-09. Analyticity of the Stokes semigroup in spaces of bounded functions in ACTA MATHEMATICA
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    http://scigraph.springernature.com/pub.10.1007/s00220-019-03344-4

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    http://dx.doi.org/10.1007/s00220-019-03344-4

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    https://app.dimensions.ai/details/publication/pub.1112703024


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