Twisting in Hamiltonian flows and perfect fluids

Stability in context of PDEs (35B35) Parallel shear flows in hydrodynamic stability (76E05) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Exponential growth of the vorticity gradient for the Euler equation on the torus
Small scale creation for solutions of the incompressible two-dimensional Euler equation
Transport and instability for perfect fluids
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
Infinite superlinear growth of the gradient for the two-dimensional Euler equation
Nonlinear stability of circular vortex patches
Wandering solutions of Euler's D-2 equation
Generalized fluid flows, their approximation and applications
Uniformly rotating analytic global patch solutions for active scalars
Global regularity for vortex patches
Bounds on the growth of the support of a vortex path
Steady asymmetric vortex pairs for Euler equations
Small-scale creation for solutions of the SQG equation
Stability of monotone, nonnegative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches
On maximally mixed equilibria of two-dimensional perfect fluids
Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole
Conjugate and cut points in ideal fluid motion
Stability of radially symmetric, monotone vorticities of 2D Euler equations
The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms
Global, local and dense non-mixing of the 3D Euler equation
Growth of perimeter for vortex patches in a bulk
The diameter of the symplectomorphism group is infinite
Boundary regularity of rotating vortex patches
Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
Groups of diffeomorphisms and the motion of an incompressible fluid
Geometric hydrodynamics in open problems
On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid
A Simple Energy Pump for the Surface Quasi-geostrophic Equation
Far-field perturbations of vortex patches
Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
Loss of Smoothness and Inherent Instability of 2D Inviscid Fluid Flows
Regularity and Blow up for Active Scalars
Stability in 𝐿¹ of circular vortex patches
Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation
Nonlinear Stability of Vortex Patches
The repeated filamentation of two-dimensional vorticity interfaces
Structure of the group of homeomorphisms preserving a good measure on a compact manifold
Generic Properties of Eigenfunctions
AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
Evolution of singularities, generalized Liapunov function and generalized integral for an ideal incompressible fluid
Conjugate points in $\mathcal {D}_{\mu }(T^2)$
Topological Methods in Hydrodynamics
On singular vortex patches, II: Long-time dynamics
Time quasi-periodic vortex patches of Euler equation in the plane
Singularity formation in the incompressible Euler equation in finite and infinite time

This page was built for publication: Twisting in Hamiltonian flows and perfect fluids