Small scale creation for solutions of the incompressible two-dimensional Euler equation

From MaRDI portal
Publication:483236

DOI10.4007/annals.2014.180.3.9zbMath1304.35521arXiv1310.4799OpenAlexW2962679132MaRDI QIDQ483236

Alexander Kiselev, Vladimír Šverák

Publication date: 16 December 2014

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4799




Related Items

Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flowConstruction of high regularity invariant measures for the 2D Euler equations and remarks on the growth of the solutionsA characteristic mapping method for the two-dimensional incompressible Euler equationsOne-dimensional model equations for hyperbolic fluid flowGlobal existence and stability for the 2D Oldroyd-B model with mixed partial dissipationAspects of PDEs Related to Fluid FlowsStability of blowup for a 1D model of axisymmetric 3D Euler equationOn the rate of merging of vorticity level sets for the 2D Euler equationsThe vanishing viscosity limit in the presence of a porous mediumA potential two-scale traveling wave singularity for 3D incompressible Euler equationsOn the global stability of a beta-plane equationActive vector models generalising 3D Euler and electron–MHD equationsStability and large-time behavior for the 2D Boussineq system with horizontal dissipation and vertical thermal diffusionStabilization and exponential decay for 2D Boussinesq equations with partial dissipationLocal ill-posedness of the incompressible Euler equations in \(C^1\) and \(B^1_{\infty,1}\)On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equationsRemark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a cornerFinite time singularity for the modified SQG patch equationOn Rayleigh-Taylor instability in nonhomogeneous incompressible elasticity fluidsIll-posedness for the incompressible Euler equations in critical Sobolev spacesThe exponential map of the group of area-preserving diffeomorphisms of a surface with boundaryGlobal Regularity for a Nonlocal PDE Describing Evolution of Polynomial Roots Under DifferentiationFinite-time singularity formation for strong solutions to the Boussinesq systemA simple ill-posedness proof for incompressible Euler equations in critical Sobolev spacesStability of perturbations near a background magnetic field of the 2D incompressible MHD equations with mixed partial dissipationInstability of unidirectional flows for the 2D \(\alpha\)-Euler equationsOn the interior regularity of weak solutions to the 2-D incompressible Euler equationsGlobal regularity for the generalized incompressible Oldroyd-B model with only stress tensor dissipation in critical Besov spacesGlobal regularity for several incompressible fluid models with partial dissipationNo local double exponential gradient growth in hyperbolic flow for the 2d Euler equationSmall scale formations in the incompressible porous media equationMicrolocal analysis of singular measuresStability of 2D inviscid MHD equations with only vertical magnetic diffusion on T2Turbulent cascades for a family of damped Szegő equationsThe stability and decay for the 2D incompressible Euler-like equationsFinite time blow up in the hyperbolic Boussinesq systemOn magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: global existence of large solutionsUniform Bound of the Highest-Order Energy of the 2D Incompressible ElastodynamicsSingularity formation in fractional Burgers' equationsAsymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equationsOn the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipationNon uniform rotating vortices and periodic orbits for the two-dimensional Euler equationsSingular Solutions for Nonlocal Systems of Evolution Equations with Vorticity StretchingGlobal well-posedness for MHD equations with magnetic diffusion and damping term in \(\mathbb{R}^2\)On nonexistence of splash singularities for the \(\alpha\)-SQG patchesA Note on Singularity Formation for a Nonlocal Transport Equation (Research)Blowup with vorticity control for a 2D model of the Boussinesq equationsUniformly rotating smooth solutions for the incompressible 2D Euler equationsOn singular vortex patches, II: Long-time dynamicsStabilization of a Background Magnetic Field on a 2 Dimensional Magnetohydrodynamic FlowStability and large-time behavior of the 2D Boussinesq equations with partial dissipationStrong ill-posedness of logarithmically regularized 2D Euler equations in the borderline Sobolev spaceGrowth of perimeter for vortex patches in a bulkLoss of regularity for the 2D Euler equationsStability and exponential decay for the 2D anisotropic Navier-Stokes equations with horizontal dissipationInviscid damping near the Couette flow in a channelA fluid mechanic’s analysis of the teacup singularityStabilizing Phenomenon for 2D Anisotropic Magnetohydrodynamic System near a Background Magnetic FieldCusp formation for a nonlocal evolution equationAn incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equationsFinite time blow up for a 1D model of 2D Boussinesq systemGlobal regularity and fast small-scale formation for Euler patch equation in a smooth domainOn the asymptotic stability of stationary solutions of the inviscid incompressible porous medium equationLinear inviscid damping and vorticity depletion for shear flowsFinite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundaryOptimal decay estimates for 2D Boussinesq equations with partial dissipationStability of hydrostatic equilibrium to the 2D Boussinesq systems with partial dissipationGevrey regularity for the Vlasov-Poisson systemThe Cauchy-Lagrangian method for numerical analysis of Euler flowSmall-scale creation for solutions of the SQG equationOn the local existence and blow-up for generalized SQG patchesOn the effects of advection and vortex stretching\(L^\infty\) ill-posedness for a class of equations arising in hydrodynamicsBoundary layer models of the Hou-Luo scenarioVortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equationsThe incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domainStabilizing effect of elasticity on the motion of viscoelastic/elastic fluidsDamping effects in boundary layers for rotating fluids with small viscosityFinite-time singularity formation for \(C^{1,\alpha}\) solutions to the incompressible Euler equations on \(\mathbb{R}^3\)A local analysis of the axisymmetric Navier–Stokes flow near a saddle point and no-slip flat boundaryFinite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equationsHigh Reynolds number and high Weissenberg number Oldroyd-B model with dissipationOn vorticity gradient growth for the axisymmetric 3D Euler equations without swirlSharp decay estimates for Oldroyd-B model with only fractional stress tensor diffusionInfluence of a background magnetic field on a 2D magnetohydrodynamic flowAnalysis of a singular Boussinesq modelStability of the Couette flow at high Reynolds numbers in two dimensions and three dimensionsFormation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided StudyGlobal well-posedness to the two-dimensional incompressible vorticity equation in the half planePreservation of log-Hölder coefficients of the vorticity in the transport equationSlipping flows and their breakingThe centrally symmetric \(V\)-states for active scalar equations. two-dimensional Euler with cut-offThe mean-field approximation for higher-dimensional Coulomb flows in the scaling-critical L spaceSelf-similar singularity of a 1D model for the 3D axisymmetric Euler equationsThe stabilizing effect of the temperature on buoyancy-driven fluidsBlow up for the 2D Euler equation on some bounded domainsMean-field convergence of point vortices to the incompressible Euler equation with vorticity in \(L^\infty\)On Singular Vortex Patches, I: Well-posedness IssuesLocal Regularity for the Modified SQG Patch EquationStabilizing effect of the magnetic field and large-time behavior of 2D incompressible MHD system with vertical dissipationPotential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity CoefficientsOptimal decay for the 2D anisotropic Navier-Stokes equations with mixed partial dissipationAxi-symmetric solutions for active vector models generalizing 3D Euler and electron-MHD equationsMagnetic relaxation of a Voigt-MHD systemStrong ill-posedness for SQG in critical Sobolev spacesPotential singularity of the 3D Euler equations in the interior domainPotentially singular behavior of the 3D Navier-Stokes equationsSingularity formation in the incompressible Euler equation in finite and infinite time



Cites Work


This page was built for publication: Small scale creation for solutions of the incompressible two-dimensional Euler equation