Related papers: On volume preserving almost Anosov flows

The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak…

In the first part of this paper, we develop the theory of anisotropic curvature measures for convex bodies in the Euclidean space. It is proved that any convex body whose boundary anisotropic curvature measure equals a linear combination of…

In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a $C^2$ open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for…

We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an…

Thanks to a recent result by Jean-Marc Schlenker, we establish an explicit linear inequality between the normalized entropies of pseudo-Anosov automorphisms and the hyperbolic volumes of their mapping tori. As its corollaries, we give an…

We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of…

We prove uniform linear bounds on the volume variation under drilling and filling operations on finite volume hyperbolic 3-manifolds.

We study $C^1$-generic vector fields on closed manifolds without points accumulated by periodic orbits of different indices and prove that they exhibit finitely many sinks and sectional-hyperbolic transitive Lyapunov stable sets with…

We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain $\mathbb T\times \mathbb R$. We prove a bound for general nonlinear interactions, which, for several fluid equations, reduces the…

We analyse a bi-fluid isentropic compressible Navier-Stokes system with barotropic pressure laws in a two-phase framework with equal pressure and single velocity. We focus on the rigorous analysis of the low Mach number limit under…

We study the long time behavior of the volume preserving $p$-flow in $\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. By extending Andrews' technique for the flow along the affine normal, we prove that every centrally symmetric solution to…

Using the quotient bundle introduced by Wojtkowski, we give necessary and sufficient conditions for a magnetic flow on a closed, oriented surface to be Anosov.

Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested…

We prove that in a $C^1$-open and $C^k$-dense set of some classes of $C^k$ Anosov flows all Lyapunov exponents have multiplicity 1 with respect to appropriate measures. The classes are geodesic flows with equilibrium states of…

In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus $\mathbb T^n$ in low dimensions $n=3,4$. The result says roughly that if the initial set is near to a strictly stable set…

We study Sobolev regularity disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. Our goal is to estimate how the stability threshold scales in…

In this note we compute the threshold regularity for meromorphic continuation of the Pollicott--Ruelle resolvent of an Anosov flow as an operator on anisotropic Sobolev spaces, in the setting of lifts to general vector bundles. These…

We prove effective equidistribution theorems for (weighted) packets of closed periodic orbits for Anosov flows. In particular, for the case of contact Anosov flows on three-dimensional manifolds, we show that the Bowen packets…

In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with…

We study the motion of sets by anisotropic curvature under a volume constraint in the plane. We establish the exponential convergence of the area-preserving anisotropic flat flow to a disjoint union of Wulff shapes of equal area, the…