Related papers: Dimension reduction for the full Navier-Stokes-Fou…
We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the…
In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…
The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. In contrast…
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
We consider the compressible Navier - Stokes - Fourier - Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer $ \Omega_{\epsilon} = \omega \times (0,\epsilon) $, where $\omega$ is a…
This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…
The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following…
In this paper, we consider a two-phase flow model consisting of the compressible Navier-Stokes systems with degenerate viscosity coupled with the compressible Navier-Stokes systems with constant viscosities via a drag force, which can be…
We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to…
We consider the Navier-Stokes-Fourier system on an unbounded domain in the Euclidean space $R^3$, supplemented by the far field conditions for the phase variables, specifically: $\rho \to 0,\ \vartheta \to \vartheta_\infty, \ u \to 0$ as $\…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
Large weak solutions to Navier--Stokes--Maxwell systems are not known to exist in their corresponding energy space in full generality. Here, we mainly focus on the three-dimensional setting of a classical incompressible…
We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…