相关论文: Nonlocal Stokes-Vlasov system: Existence and deter…
We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…
The purpose of this paper is to study the existence, uniqueness and lifespan of solutions for a fractional Stokes-Transport system. This problem should be understood as a model for sedimentation in a fluid where the viscosity law is given…
In this paper, we study the three-dimensional non-isentropic compressible fluid-particle flows. The system involves coupling between the Vlasov-Fokker-Planck equation and the non-isentropic compressible Navier-Stokes equations through…
A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the…
In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^{3}\times\mathbb{R}^{3}$, where the initial fluid density is allowed to vanish. We establish the uniform bound of…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
We consider the Cauchy problem for coupled system of Vlasov and non-Newtonian fluid equations. We establish local well--posedness of the strong solutions, provided that the initial data are regular enough. Global existence of unique strong…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
This paper derives the stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients. By means of weak convergence method and Stratonovich--Khasminskii averaging principle approach, the solution of two…
Stokes variational inequalities arise in the formulation of glaciological problems involving contact. We consider the problem of a two-dimensional marine ice sheet with a grounding line, although the analysis presented here is extendable to…
Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…
Probing dynamic and static correlation in glass-forming supercooled liquids has been a challenge for decades in spite of extensive research. Dynamic correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a vast variety…
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centres, valid at all separations. This goes beyond the applicable range of…
We investigate the nonlocal version of the Abels-Garcke-Gr\"{u}n (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
We analyze the system of equations describing the flow of a dilute particle system coupled with an incompressible non-Newtonian fluid in a bounded domain. In this setting, both PDEs are connected via a drag force, or the friction force. We…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast…
Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique developed for simulating complex fluid flows. Among its key ingredients is the use of nonlocal integral relaxations to local differentiations. Mathematical analysis of…