Related papers: Shrinking targets problems for flows on homogeneou…
We study singularity formation for the heat flow of harmonic maps from $\R^d$. For each $d \geq 4$, we construct a compact, $d$-dimensional, rotationally symmetric target manifold that allows for the existence of a corotational self-similar…
We study the following control problem. A fish with bounded aquatic locomotion speed swims in fast waters. Can this fish, under reasonable assumptions, get to a desired destination? It can, even if the flow is time-dependent. Moreover,…
We consider the problem of asymptotic stability and linear inviscid damping for perturbations of a point vortex and similar degenerate circular flows. Here, key challenges include the lack of strict monotonicity and the necessity of working…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension…
In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the…
This paper studies the fundamental problem of how to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast. This scheduling…
Discrete-time dynamical systems can be derived from group actions. In the present work possibility of application of this method to systems of ordinary differential equations is studied. Invertible group actions are considered as possible…
Let $D$ be a directed graph cellularly embedded in a surface together with non-negative cost on its arcs. Given any integer circulation in $D$, we study the problem of finding a minimum-cost non-negative integer circulation in $D$ that is…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence…
In this paper, we consider a family of closed hypersurfaces which shrink self-similarly with speed of quotient curvatures. We show that the only such hypersurfaces are shrinking spheres.
We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a…