A continuation principle for the 3-D Euler equations for incompressible fluids in a bounded domain

DOI10.3792/pjaa.69.77zbMath0790.35086OpenAlexW1993636305MaRDI QIDQ1312060

Taku Yanagisawa, Taira Shirota

Publication date: 26 June 1994

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.69.77

zbMATH Keywords

Euler equationssmooth solutioninitial boundary value problembounded domainlocal in time existence theorembreakdown of smooth solutionsaccumulation of the vorticityharmonic integralsideal incompressible fluids

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) A priori estimates in context of PDEs (35B45) Applications of functional analysis to differential and integral equations (46N20)

Related Items (18)

On blow-up criteria of smooth solutions to the 3-D Euler equations in a bounded domain. ⋮ Viscous approximations and decay rate of maximal vorticity function for 3D axisymmetric Euler equations ⋮ A regularity criterion for the Keller-Segel-Euler system ⋮ Precise regularity results for the Euler equations. ⋮ A blow‐up criterion to a Keller–Segel system coupled with the Euler fluid ⋮ The 3D incompressible Euler equations with a passive scalar: a road to blow-up? ⋮ On the breakdown of 2D compressible Eulerian flows in bounded impermeable regions with corners ⋮ Brezis-Gallouet-Wainger type inequalities and blow-up criteria for Navier-Stokes equations in unbounded domains ⋮ Global regularity for a 2D model of electro-kinetic fluid in a bounded domain ⋮ Brezis-Gallouet-Wainger type inequality and its application to the Navier-Stokes equations ⋮ Regularity criteria for the incompressible magnetohydrodynamic equations with partial viscosity ⋮ Note on global existence for axially symmetric solutions of the Euler system ⋮ Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain ⋮ A new path to the non blow-up of incompressible flows ⋮ Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study ⋮ Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation ⋮ Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations ⋮ On the blow-up of solutions of the 3-D Euler equations in a bounded domain

Cites Work

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• Nonlinear evolution equations and the Euler flow
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• On the blow-up of solutions of the 3-D Euler equations in a bounded domain
• Remarks on the Euler equation
• On Green's matrices for elliptic boundary value problems. II
• A Concise Presentation of the Euler Equations of Hydrodynamics
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

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