Related papers: Exit times of diffusions with incompressible drift
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
We revisit the issue of Lagrangian irreversibility in the context of recent results [Xu, et al., PNAS, 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are…
We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…
We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R^d and infinity. The study of maximal flow is…
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial…
The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial…
We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. We assume that the initial velocity is a finite-energy and L^q-summable perturbation of the Oseen vortex with…
We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)^{-b} with exponent depending on the…
In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and…
This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed…
Let $0\le u_0(x)\in L^1(\R^2)\cap L^{\infty}(\R^2)$ be such that $u_0(x) =u_0(|x|)$ for all $|x|\ge r_1$ and is monotone decreasing for all $|x|\ge r_1$ for some constant $r_1>0$ and ${ess}\inf_{\2{B}_{r_1}(0)}u_0\ge{ess}…
We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation then to minimum-domain form, and from incompressible to compressible flows. For incompressible flow, the minimum-domain…
Swimmers caught in a rip current flowing away from the shore are advised to swim orthogonally to the current to escape it. We describe a mathematical principle in a similar spirit. More precisely, we consider flows $\gamma$ in the plane…
In this paper, we prove the global wellposedness of the Navier-Stokes equations describing a motion of compressible, viscous, barotropic fluid flow in a 3 dim. exterior domain in the $L_p$ in time and $L_2 \cap L_6$ maximal regularity…
This paper addresses a problem in experimental design: We consider It\^o diffusions specified by some $\theta \in \mathbb{R}$ and assume that we are allowed to observe their sample paths only $n$ times before a terminal time $\tau <…
The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved…