Related papers: Weak mixing for area preserving flows on surfaces
This is a survey of recent advances in the study of chaotic and spectral properties of smooth area-preserving flows on surfaces, written in occasion of a plenary talk given at the XXI Congress of the Italian Mathematical Union, in Pavia in…
We study the evolution of a weakly convex surface $\Sigma_0$ in $\R^3$ with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the…
We consider special flows over two-dimensional rotations by $(\alpha,\beta)$ on $\T^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition $\int_{\T^2}f_x(x,y)\,dx\,dy\neq 0\neq \int_{\T^2}f_y(x,y)\,dx\,dy.$ Such…
We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…
We establish strong mixing for the $\mathbb Z^d$-periodic, infinite horizon, Lorentz gas flow for continuous observables with compact support. The essential feature of this natural class of observables is that their support may contain…
The paper investigates quantitative weak mixing of Salem substitutions flows. We prove that for a substitution whose substitution matrix is irreducible over the rationals and the dominant eigenvalue is a Salem number, for almost every…
Mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary. As a measure of the efficiency of stirring, the bulk scalar concentration variance is bounded and the bound…
We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some…
We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the flow); thus, provide weak formulations that are generalized to…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
We propose a weak form of domination, called partially dominated splitting and the main result is that there is a partially dominated splitting over a nonsingular compact invariant set for a flow if, and only if, the associated linear…
We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the…
We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…
We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians…
The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight-biding regime. For the case of half flux per plaquette, and for a wide range of values of the…
This paper is concerned with the existence of global-in-time weak solutions to the multicomponent reactive flows inside a moving domain whose shape in time is prescribed. The flow is governed by the 3D compressible Navier-Stokes-Fourier…
We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate saddles and that is nevertheless not mixing.
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that…
In this note we show that a weakly geometrically flat map $\pi$ : M $\rightarrow$ N between pure dimensional complex spaces has the local lifting property for cycles. From this result we also deduce that, under these hypotheses, several…
We study Brownian flows on manifolds for which the associated Markov process is strongly mixing with respect to an invariant probability measure and for which the distance process for each pair of trajectories is a diffusion $r$. We provide…