Uniformly rotating analytic global patch solutions for active scalars
From MaRDI portal
Publication:1661378
DOI10.1007/s40818-016-0007-3zbMath1397.35020arXiv1508.01655OpenAlexW2219875148MaRDI QIDQ1661378
Javier Gómez-Serrano, Angel Castro, Diego Cordoba
Publication date: 16 August 2018
Published in: Annals of PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1508.01655
Related Items
Multipole Vortex Patch Equilibria for Active Scalar Equations ⋮ On the stability of discrete tripole, quadrupole, Thomson' vortex triangle and square in a two-layer/homogeneous rotating fluid ⋮ Active vector models generalising 3D Euler and electron–MHD equations ⋮ Degenerate bifurcation of the rotating patches ⋮ Bifurcation of rotating patches from Kirchhoff vortices ⋮ Global solutions of a surface quasigeostrophic front equation ⋮ Existence of small loops in a bifurcation diagram near degenerate eigenvalues ⋮ Existence of stationary vortex sheets for the 2D incompressible Euler equation ⋮ Vortex rigid motion in quasi-geostrophic shallow-water equations ⋮ Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc ⋮ Mini-workshop: Free boundary problems arising in fluid mechanics. Abstracts from the mini-workshop held February 26 -- March 4, 2023 ⋮ Time Periodic Doubly Connected Solutions for the 3D Quasi-Geostrophic Model ⋮ A note on the existence of stationary vortex patches for the SQG equation in bounded domain ⋮ Non uniform rotating vortices and periodic orbits for the two-dimensional Euler equations ⋮ Global solutions for the generalized SQG patch equation ⋮ Time quasi-periodic vortex patches of Euler equation in the plane ⋮ On the rapidly rotating vorticity in the unit disk ⋮ Traveling waves near Couette flow for the 2D Euler equation ⋮ Global bifurcation for corotating and counter-rotating vortex pairs ⋮ Uniformly rotating smooth solutions for the incompressible 2D Euler equations ⋮ Imperfect bifurcation for the quasi-geostrophic shallow-water equations ⋮ On the existence of stationary patches ⋮ Contour dynamics for surface quasi-geostrophic fronts ⋮ Global Smooth Solutions for the Inviscid SQG Equation ⋮ Existence of corotating and counter-rotating vortex pairs for active scalar equations ⋮ Steady asymmetric vortex pairs for Euler equations ⋮ On radial symmetry of rotating vortex patches in the disk ⋮ Relative equilibria with holes for the surface quasi-geostrophic equations ⋮ On the estimate of distance traveled by a particle in a disk-like vortex patch ⋮ On the local existence and blow-up for generalized SQG patches ⋮ Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation ⋮ Vortex patches choreography for active scalar equations ⋮ Doubly Connected $V$-States for the Planar Euler Equations ⋮ Kármán vortex street in incompressible fluid models ⋮ The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces ⋮ Symmetry in stationary and uniformly rotating solutions of active scalar equations ⋮ The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge ⋮ Computer-assisted proofs in PDE: a survey ⋮ Stability and instability of Kelvin waves ⋮ Uniqueness for SQG patch solutions ⋮ Quantitative estimates for uniformly-rotating vortex patches ⋮ Time periodic solutions for 3D quasi-geostrophic model ⋮ On Singular Vortex Patches, I: Well-posedness Issues ⋮ Global solutions for the generalized SQG equation and rearrangements
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Remarks on geometric properties of SQG sharp fronts and \(\alpha\)-patches
- The stability of rotating vortex patches
- Steady-state solutions of the Euler equations in two dimensions: Rotating and translating V-states with limiting cases. I: Numerical algorithms and results
- An efficient and general numerical method to compute steady uniform vortices
- On the evolution of nearly circular vortex patches
- Motions of vortex patches
- Dynamics near an unstable Kirchhoff ellipse
- Global regularity for vortex patches
- On the V-states for the generalized quasi-geostrophic equations
- On rotating doubly connected vortices
- The sharp corner formation in 2D Euler dynamics of patches: infinite double exponential rate of merging
- The centrally symmetric \(V\)-states for active scalar equations. two-dimensional Euler with cut-off
- Boundary regularity of rotating vortex patches
- Existence for the \(\alpha \)-patch model and the QG sharp front in Sobolev spaces
- Bifurcation from simple eigenvalues
- Doubly Connected $V$-States for the Planar Euler Equations
- A scenario for finite-time singularity in the quasigeostrophic model
- Generalized surface quasi-geostrophic equations with singular velocities
- Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
- Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
- Stability of vortices in equilibrium with a cylinder
- The stability and energetics of corotating uniform vortices
- Nonlinear Stability of Vortex Patches
- A new family of uniform vortices related to vortex configurations before merging
- On the evolution of sharp fronts for the quasi‐geostrophic equation
- The nonlinear evolution of rotating configurations of uniform vorticity
- The evolution of Kirchhoff elliptic vortices
- Evidence of singularities for a family of contour dynamics equations