English
Related papers

Related papers: Manifold Solutions to Navier-Stokes Equations

200 papers

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…

Numerical Analysis · Mathematics 2023-10-16 Maxim A. Olshanskii , Arnold Reusken , Paul Schwering

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…

Analysis of PDEs · Mathematics 2023-12-01 Yongqian Han

The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit…

Mathematical Physics · Physics 2007-05-23 R. M. Kiehn

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a…

High Energy Physics - Theory · Physics 2009-08-24 Sayantani Bhattacharyya , Shiraz Minwalla , Spenta R. Wadia

We utilize undetermined coefficient method and an iterative method to construct the series solutions of the 3D Cauchy problem for a class of incompressible Navier-Stokes and Euler Equations. Then we can turn the Navier-Stokes Equations…

Analysis of PDEs · Mathematics 2016-02-01 Tao Zhang , Alatancang

We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R^2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing…

Analysis of PDEs · Mathematics 2009-11-07 Th. Gallay , C. E. Wayne

We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…

Analysis of PDEs · Mathematics 2019-07-23 Wojciech M. Zajaczkowski

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

In that report solution to incompressible Navier - Stokes equations in non - dimensional form will be presented. Standard fundamental methods: SIMPLE, SIMPLER (SIMPLE Revised) and Vorticity-Stream function approach are compared and results…

Fluid Dynamics · Physics 2007-05-23 Maciej Matyka

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…

Numerical Analysis · Mathematics 2018-02-14 Sebastian Reuther , Axel Voigt

We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such…

Analysis of PDEs · Mathematics 2022-05-05 YanYan Li , Zhuolun Yang

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…

Analysis of PDEs · Mathematics 2023-11-21 Hirokazu Saito , Yoshihiro Shibata

In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable…

Analysis of PDEs · Mathematics 2024-12-10 Brian David Vasquez Campos

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete…

Numerical Analysis · Mathematics 2026-05-05 Takeharu Matsuda , Satoshi Ii

The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…

Analysis of PDEs · Mathematics 2022-03-04 Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

The existence of global regular axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder is proved. The main step in the proof is a proof of the Holder continuity of the swirl. This gives a possibility to prove…

Analysis of PDEs · Mathematics 2013-03-06 Wojciech Zajaczkowski

In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].

Analysis of PDEs · Mathematics 2013-08-20 Dongsheng Li

The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…

Computational Physics · Physics 2022-11-22 Alejandro Quirós Rodríguez , Tomas Fullana , Vincent Le Chenadec , Taraneh Sayadi

A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…

Fluid Dynamics · Physics 2016-08-30 Alexey V. Zhirkin

These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…

Analysis of PDEs · Mathematics 2026-04-16 Athanasios E. Tzavaras