相关论文: Global bounded solution in three-dimensional chemo…

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…

This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…

The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…

We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as…

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in…

In this manuscript, we aim to establish global existence of weak solutions with higher regularity to the compressible Navier-Stokes equations under no-slip boundary conditions. Though Lions\cite{L1} and Feireisl\cite{F1} have established…

We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.

This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an $L^2$ maximum principle for the fluid interface. We also show global in time existence for strong and weak…

This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We showed the existence of the boundary layer in different areas. By employing the energy method, we also…

A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…

Note: The final version of this article was published in Computers and Geosciences, Volume 206, January 2026, 106038. DOI: 10.1016/j.cageo.2025.106038. Readers should refer to the published version for the most up-to-date content.…

In this paper we study the problem of the global existence (in time) of weak, entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase…

This paper investigates the connection between the chemotaxis--Navier--Stokes system with porous medium type nonlinear diffusion and the Hele--Shaw problem in $\mathbb{R}^d$ ($d\geq2$). First, we prove the global-in-time existence of weak…

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…

We consider electrodiffusion of ions in fluids, described by the Nernst-Planck-Navier-Stokes system, in three dimensional bounded domains, with mixed blocking (no-flux) and selective (Dirichlet) boundary conditions for the ionic…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…