Related papers: Global weak solutions for a two-component Novikov …
We consider inverse boundary value problems for the Navier-Stokes equations and the isotropic Lam\'e system in two dimensions. The uniqueness without any smallness assumptions on unknown coefficients, which is called global uniqueness, was…
We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…
This paper is devoted to global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models with center diffusion. By virtue of the properties of Calderon-Zygmund operator and the Littlewood-Paley decomposition…
Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space…
We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation…
We prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the product of the maximal and minimal slopes is strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$…
This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term $n_t + u\cdot\nabla n =\Delta n^m - \chi\nabla\cdot(n\nabla c) + \kappa n -\mu n^2$, $x \in \Omega,\ t>0$, $c_t + u\cdot\nabla c = \Delta c…
We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
In this paper, we study the global well-posedness and decay rates of strong solutions to an incompressible Vlasov-MHD model arising in magnetized plasmas. This model is consist of the Vlasov equation and the incompressible…
In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique,…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
We derive the global existence of weak solutions of the Shigesada-Kawasaki-Teramoto systems in space dimension less or equal to 4 with a rather general condition on the coefficients. The existence is established using finite differences in…
Proving the uniqueness of solutions to multi-species cross-diffusion systems is a difficult task in the general case, and there exist very few results in this direction. In this work, we study a particular system with zero-flux boundary…
We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions, with the initial data taken as small $L^\infty$…
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an…
We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity…