相关论文: Renormalization for autonomous nearly incompressib…
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…
We study selection by vanishing viscosity for the transport of a passive scalar $f(x,t)\in\mathbb{R}$ advected by a bounded, divergence-free vector field $u(x,t)\in\mathbb{R}^2$. This is described by the initial value problem to the PDE…
In this paper we study the solvability of different boundary value problems for the two dimensional steady incompressible Euler equation. Two main methods are currently available to study those problems, namely the Grad-Shafranov method and…
We consider the inverse problem for the general transport equation with external field, source term and absorption coefficient. We show that the source and the absorption coefficients can be uniquely reconstructed from the boundary…
We construct global-in-time, unique solutions of the two-dimensional Euler equations in a Yudovich type space and a $\rm bmo$-type space. First, we show the regularity of solutions for the two-dimensional Euler equations in the Spanne space…
We prove weak existence of Euler equation (or Navier-Stokes equation) perturbed by a multiplicative noise on bounded domains of $\mathbb R^2$ with Dirichlet boundary conditions and with periodic boundary conditions. Solutions are $H^1$…
We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with $BV$ vector-fields that have divergence in $L^\infty$ (or in $L^1$) and that are nearly incompressible (see the text for…
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a…
In this work, we study the doubly degenerate nutrient taxis system with logistic source \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ u - u^2, \\…
In the present work, we establish space Bounded Variation $(BV)$ regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed…
We study the nonlocal vectorial transport equation $\partial_ty+ (\mathbb{P} y \cdot \nabla) y=0$ on bounded domains of $\mathbb{R}^d$ where $\mathbb{P}$ denotes the Leray projector. This equation was introduced to obtain the unique optimal…
We consider two-dimensional autonomous divergence free vector-fields in $\Lde_{loc}$. Under a condition on direction of the flow and on the set of critical points, we prove the existence and uniqueness of a stable a.e. flow and of…
This paper is concerned with the Dirichlet initial-boundary value problem of a 2-D parabolic-elliptic system proposed to model the formation of biological transport networks. Even if global weak solutions for this system are known to exist,…
We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator estimates, we gain the existence and uniqueness of…
Stability of the value function and the set of minimizers w.r.t. the given data is a desirable feature of optimal transport problems. For the classical Kantorovich transport problem, stability is satisfied under mild assumptions and in…
Without any smallness assumption, we prove the global unique solvability of the 2-D incompressible inhomogeneous Navier-Stokes equations with initial data in the critical Besov space, which is almost the energy space in the sense that they…
We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly…
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…
This paper is concerned with the existence of globally smooth solutions for the second boundary value problem for Monge-Ampere equations and the application to regularity of potentials in optimal transportation. The cost functions satisfy a…
We consider the stochastic transport equation with a possibly unbounded H\"older continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of W^{1,p}-weak solutions.