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Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.


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Journal ArticleDOI
TL;DR: In this article, a new set of equations termed the augmented Burnett equations was developed and shown to be stable both by a linearized stability analysis and by direct numerical computations for one-dimensional and plane-two-dimensional flows.
Abstract: Numerical solutions of the Burnett equations for hypersonic flow at high altitudes in the continuum transitional regime were not possible except for some one-dimensional flows. It is shown from both analytical investigation and numerical computations that the Burnett equations are unstable to disturbances of small wavelengths. This fundamental instability arises in numerical computations when the grid spacing is less than the order of a mean free path and precludes Burnett flowfield computations above a certain maximum altitude for any given aerospace vehicle. A new set of equations termed the "augmented Burnett equations" has been developed and shown to be stable both by a linearized stability analysis and by direct numerical computations for one-dimensional and plane-two-dimensional flows. The latter represents the first known Burnett solutions for two-dimensional hypersonic flow over blunt leading edges. The comparison of these solutions with the conventional Navier-Stokes solutions reveals that the difference is small in low-altitude low-speed flows but significant in high-altitude hypersonic flows.

137 citations

Journal ArticleDOI
TL;DR: A new estimate of solutions for the Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations is explored by taking advantage of a coupling structure of the equations and using a scale decomposition technique.
Abstract: In this paper, we investigate the Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. By taking advantage of a coupling structure of the equations and using a scale decomposition technique, we explore a new estimate of solutions. This estimate together with a microlocal analysis entails the global existence and uniqueness of weak solutions to the chemotaxis-Navier--Stokes system for a large class of initial data.

136 citations

Journal ArticleDOI
TL;DR: In this article, a condition of local Holder continuity for suitable weak solutions to the Navier-Stokes equations near the plane boundary has been proved, in the form of the Caffarelli-Kohn-Nirenberg condition.
Abstract: We prove a condition of local Holder continuity for suitable weak solutions to the Navier—Stokes equations near the plane boundary. This condition has the form of the Caffarelli—Kohn—Nirenberg condition for local boundedness of suitable weak solutions at the interior points of the space-time cylinder.

136 citations

Journal ArticleDOI
TL;DR: In this article, the authors prove global existence of appropriate weak solutions for the compressible Navier-Stokes equations for more general stress tensors than those covered by P. Lions and E. Feireisl's theory.
Abstract: We prove global existence of appropriate weak solutions for the compressible Navier–Stokes equations for more general stress tensor than those covered by P.–L. Lions and E. Feireisl’s theory. More precisely we focus on more general pressure laws which are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events (virial pressure law), geophysical flows (eddy viscosity) or biological situations (anisotropy).

136 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023183
2022389
2021544
2020509
2019545
2018575