Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form

DOI10.1017/S0022112089001357zbMath0674.76013OpenAlexW2138131297MaRDI QIDQ3829205

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Publication date: 1989

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112089001357

zbMATH Keywords

Navier-Stokes equationsinitial-value problemLagrangian coordinatesinfinite domainclassic, two-dimensional stagnation-point solutionunbounded initial vorticity

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Vortex flows for incompressible inviscid fluids (76B47) Navier-Stokes equations (35Q30) Basic methods in fluid mechanics (76M99)

Related Items (29)

Geometry of singularities for the steady Boussinesq equations ⋮ Dynamos in an annulus with fields linear in the axial coordinate ⋮ On some classes of nonstationary axially symmetric solutions to the Navier-Stokes equations ⋮ The generalized Proudman-Johnson equation revisited ⋮ Finite-time singularity formation for strong solutions to the Boussinesq system ⋮ Blow-up of solutions to the generalized inviscid Proudman-Johnson equation ⋮ Damped infinite energy solutions of the 3D Euler and Boussinesq equations ⋮ ‘Unforced’ Navier–Stokes solutions derived from convection in a curved channel ⋮ Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers ⋮ Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition ⋮ Infinite energy solutions of the surface quasi-geostrophic equation ⋮ One-parameter solutions of the Euler-Arnold equation on the contactomorphism group ⋮ Global estimates and blow-up criteria for the generalized Hunter-Saxton system ⋮ Numerical study of singularity formation in a class of Euler and Navier–Stokes flows ⋮ The numerical study of blowup with application to a nonlinear Schrödinger equation ⋮ Global existence of solutions to the Proudman-Johnson equation ⋮ Numerical study of stagnation-point flows of incompressible fluid ⋮ The role of initial curvature in solutions to the generalized inviscid Proudman-Johnson equation ⋮ Global and singular solutions to the generalized Proudman-Johnson equation ⋮ Finite-time blowup and ill-posedness in Sobolev spaces of the inviscid primitive equations with rotation ⋮ On the Euler equations of incompressible fluids ⋮ Dynamic bifurcation in a system of PDES with a conserved first integral ⋮ Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations ⋮ On the global well-posedness of the inviscid generalized Proudman-Johnson equation using flow map arguments ⋮ Finite-time vortex singularity in a model of three-dimensional Euler flows ⋮ Singularity formation for complex solutions of the 3D incompressible Euler equations ⋮ Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics ⋮ Blowup in stagnation-point form solutions of the inviscid 2d Boussinesq equations ⋮ Riemannian geometry of the contactomorphism group

Cites Work

• Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogene, incompressible, pendant un temps infiniment long
• Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompressiblen Flüssigkeit
• On classical solutions of the two-dimensional non-stationary Euler equation

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