Related papers: On derivations of evolving surface Navier-Stokes e…
Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'function composition' approach involving local shape derivatives…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…
In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…
Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged…
The incompressible Navier-Stokes equations are considered. We find that these equations have symplectic symmetry structures. Two linearly independent symplectic symmetries form moving frame. The velocity vector possesses symplectic…
This paper is concerned with the global solvability for the Navier-Stokes equations describing viscous free surface flows of infinite depth in three and higher dimensions. We first prove time weighted estimates of solutions to a linearized…
We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].
In order to address the difficulties of classical fluid kinematics in describing vorticity and the paradox of linear correlation between viscous force and vorticity in the Navier-Stokes equations, the study examines the inherent…
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were obtained in the past one hundred years,…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…
A new arbitrary Lagrangian-Eulerian (ALE) formulation for Navier-Stokes flow on self-evolving surfaces is presented. It is based on a general curvilinear surface parameterization that describes the motion of the ALE frame. Its in-plane part…
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…
This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…
We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure…