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We study models kinetic models of polymeric fluids. We introduce a notion of solutions which is based on moments of polymeric distributions. We prove global existence and uniqueness of a large class of initial data for diffusive systems of…
We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…
We study the long-time behavior of a point mass moving in a one-dimensional viscous compressible fluid. Previously, we showed that the velocity of the point mass $V(t)$ satisfies a decay estimate $V(t)=O(t^{-3/2})$~[K. Koike, J.…
We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
In this paper, we investigate the time decay behavior to Lions weak solution of 2D incompressible density-dependent Navier-Stokes equations with variable viscosity.
We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations…
We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…
In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system…
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…
We cope with a free boundary fluid-structure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by Navier-Stokes equations while the…
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
We consider the Navier-Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by G.P. Galdi and P. Maremonti "On…
We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to…
The existence of weak solutions to the "viscous incompressible fluid + rigid body" system with Navier slip-with-friction conditions in a 3D bounded domain has been recently proved by G\'{e}rard-Varet and Hillairet in \cite{exi:GeH}. In 2D…
We consider a system of nonlinear partial differential equations modeling the unsteady motion of an incompressible generalized Newtonian fluid with chemical reactions. The system consists of the generalized Navier-Stokes equations with…
In this paper, we consider the high-Weissenberg number limit of a Voigt-regularized two-dimensional Oldroyd-B model for viscoelastic fluids. We first demonstrate that the Euler-Oldroyd-B system is both linearly and nonlinearly ill-posed in…
We study the spatial decay of time-periodic Navier-Stokes flow at the rate $|x|^{-1}$ with/without wake structure in 3D exterior domains when a rigid body moves periodically in time. In this regime the existence of time-periodic solutions…
In this study we are interested in the Navier-Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of periodic in time weak solutions to the…
The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…