A characterization of harmonic \(L^r\)-vector fields in three dimensional exterior domains

DOI10.1007/s12220-022-00938-8zbMath1498.53055OpenAlexW4280550916MaRDI QIDQ2141388

Anton Seyfert, Hideo Kozono, Taku Yanagisawa, Senjo Shimizu, Matthias Hieber

Publication date: 25 May 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-022-00938-8

zbMATH Keywords

exterior domainsBetti numbersharmonic vector fieldsjump conditionHelmholtz-Weyl decomposition

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems for second-order elliptic systems (35J57)

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The Helmholtz decomposition of a \(BMO\) type vector field in general unbounded domains ⋮ Preface

Cites Work

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• Global existence results for Oldroyd-B fluids in exterior domains: the case of non-small coupling parameters
• Multiple integrals in the calculus of variations
• Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data
• Classical solutions of the Stefan problem
• The existence and uniqueness of nonstationary ideal incompressible flow in exterior domains in \(R^ 3\)
• Manifolds, tensor analysis, and applications.
• \(L^r\)-Helmholtz-Weyl decomposition for three dimensional exterior domains
• Stationary Navier-Stokes equations under inhomogeneous boundary conditions in 3D exterior domains
• Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains
• A characterization of harmonic \(L^r\)-vector fields in two-dimensional exterior domains
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• $L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains
• Estimating ∇u by divu and curlu