Existence, uniqueness and \(L^ q\)-estimates for the Stokes problem in an exterior domain

DOI10.1007/BF02384076zbMath0722.35065MaRDI QIDQ756021

Christian G. Simader, Giovanni Paolo Galdi

Publication date: 1990

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

existenceunbounded domainsStokes equations

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic \(L^ 2\) decay for Navier-Stokes flows in exterior domains
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• On the solutions of a class of equations occurring in continuum mechanics, with application to the Stokes paradox
• Domains of fractional powers of the Stokes operator in \(L_ r\) spaces
• Estimates for solutions of nonstationary Navier-Stokes equations
• Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains
• On Dirichlet's boundary value problem. An \(L^p\)-theory based on a generalization of Garding's inequality
• Su un problema al contorno relativo al sistema di equazioni di Stokes
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• On cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

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