Related papers: Sufficiency Class for Global (in Time) Solutions t…
We prove the existence of a forward discretely self-similar solutions to the Navier-Stokes equations in $ \Bbb R^{3}\times (0,+\infty)$ for a discretely self-similar initial velocity belonging to $ L^2_{ loc}(\Bbb R^{3})$.
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler--Navier--Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two…
The purpose of this paper is to provide a large class of initial data which generates global smooth solution of the 3-D inhomogeneous incompressible Navier-Stokes system in the whole space~$\R^3$. This class of data is based on functions…
In this paper, we consider the initial-boundary value problem of three-dimensional isentropic compressible Navier-Stokes equations with rotating effect terms in an exterior domain with Navier-slip boundary condition and with far-field…
For periodic initial data with initial density, we establish the global existence and uniqueness of strong and classical solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…
In 1995, Kazhikhov and Vaigant introduced a particular class of isentropic compressible Navier-Stokes equations with variable viscosity coefficients and, for the first time, established the existence of global smooth solutions for…
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…
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 prove the existence of strong solutions to Navier-Stokes equations in three dimensional thin domains. Our proof is based on the energy and the Poincar\'e inequalities as well as contraction principle argument and is free of the mean…
In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial…
In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in water. Our main result is a weak-strong uniqueness principle…
The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyond the finite Leray-Hopf regularity interval, every…
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…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
This article is an updated version of the article that was published in the Electronic Journal of Differential Equations on 10. July 2010. Two footnotes have been added. One corrects a minor error not influencing the proof, the second is…
For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…
This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows…
We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the…
This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density ($\mu(\rho)=\mu\rho^\alpha$…