相关论文: Renormalization for autonomous nearly incompressib…

In this paper we consider the following non-linear stochastic partial differential equation (SPDE): \begin{align*} \begin{cases} \mathrm{d}u(s,x)=\sum^n_{i=1} \mathscr{L}_i u(s,x)\circ \mathrm{d}W_i(s)+\left(V(x)+\mu\Delta…

We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove…

We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we…

We prove estimates for the transport exponents associated with the weakly coupled Fibonacci Hamiltonian. It follows in particular that the upper transport exponent $\tilde \alpha^\pm_u$ approaches the value one as the coupling goes to zero.…

We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d \geq 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly-supported perturbations, where…

We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…

The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…

We prove existence and uniqueness results for solutions to a class of optimal transportation problems with infinitely many marginals, supported on the real line. We also provide a characterization of the solution with an explicit formula.…

We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the…

This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This…

We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…

We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…

The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…

We consider linear and nonlinear transport equations with irregular velocity fields, motivated by models coming from mean field games. The velocity fields are assumed to increase in each coordinate, and the divergence therefore fails to be…

The continuous dependence on the initial data and consequently the uniqueness of bounded weak solutions to a class of triangular reaction-cross-diffusion equations is shown. The class includes two-species doubly degenerate equations for…

This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded, coercive, and self-adjoint operators $\bc{A, B}: V\mapsto…

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…

We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…

We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…