Kato's perturbation theory and well-posedness for the Euler equations in bounded domains

DOI10.1007/BF00276432zbMath0672.35044OpenAlexW2114900948MaRDI QIDQ1120071

Hugo Beirão da Veiga

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf00276432

zbMATH Keywords

existenceperturbationestimateswell-posednessEuler equationsinitial datacontinuous dependencestationary problem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) First-order nonlinear hyperbolic equations (35L60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

• Nonlinear evolution equations and the Euler flow
• Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow
• On the Euler equations of incompressible perfect fluids
• A well-posedness theorem for non-homogeneous inviscid fluids via a perturbation theorem
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Linear evolution equations of hyperbolic type. II
• A Concise Presentation of the Euler Equations of Hydrodynamics
• The equations of motion of a perfect fluid with free boundary are not well posed.
• Commutator estimates and the euler and navier-stokes equations
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