Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting

DOI10.4310/DPDE.2013.v10.n1.a3zbMath1307.35189arXiv1006.2819MaRDI QIDQ2375859

Magdalena Czubak, Chi Hin Chan

Publication date: 25 June 2013

Published in: Dynamics of Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.2819

zbMATH Keywords

hyperbolic spacesLiouville theoremnon-uniquenessNavier-StokesLeray-Hopf

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01)

Related Items (17)

Homogeneous cosmologies as group field theory condensates ⋮ Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space ⋮ Periodic and almost periodic evolution flows and their stability on non-compact Einstein manifolds and applications ⋮ Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere ⋮ Rate of the enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere ⋮ The formulation of the Navier-Stokes equations on Riemannian manifolds ⋮ Asymptotically almost periodic solutions to parabolic equations on the real hyperbolic manifold ⋮ Liouville theorems for the stationary Navier-Stokes equation on a hyperbolic space ⋮ A minimal-variable symplectic method for isospectral flows ⋮ On asymptotically almost periodic solutions to the Navier-Stokes equations in hyperbolic manifolds ⋮ Turbulence on hyperbolic plane: the fate of inverse cascade ⋮ The incompressible Navier-Stokes equations on non-compact manifolds ⋮ Navier-Stokes equations in a curved thin domain. III: Thin-film limit ⋮ Nonuniqueness of solutions of the Navier-Stokes equations on Riemannian manifolds ⋮ On the well-posedness of relativistic viscous fluids with non-zero vorticity ⋮ On the stability phenomenon of the Navier-Stokes type equations for elliptic complexes ⋮ Nonlinear stability of the two-jet Kolmogorov type flow on the unit sphere under a perturbation with nondissipative part

This page was built for publication: Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting