相关论文: Global existence for some transport equations with…

We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &\theta_t+u\theta_x+\nu \Lambda^{\gamma}\theta=0, \\ & u=\mathcal{N}(\theta), \end{split} \end{equation*} where…

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

We consider 1D dissipative transport equations with nonlocal velocity field: \[ \theta_t+u\theta_x+\delta u_{x} \theta+\Lambda^{\gamma}\theta=0, \quad u=\mathcal{N}(\theta), \] where $\mathcal{N}$ is a nonlocal operator given by a Fourier…

This paper is concerned with a class of multi-dimensional transport equations with nonlocal velocity. It is shown that the local smooth solution cannot exist globally in time via the De Giorgi iteration technique.

This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…

We consider the model of viscous compressible multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which…

In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…

In this paper we study the Cauchy problem for one multidimensional compressible nonlocal model of the dissipative quasi-geostrophic equations. First, we obtain the local existence and uniqueness of the smooth non-negative solution or the…

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative,…

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…

We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compressible Navier-Stokes equations, the weak…

Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…

This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…

We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global…

We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for…

We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an…

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…

We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth…

We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…