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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, it was shown that the Navier-Stokes equations for one-dimensional, compressible flow need not depend continuously on their initial data, at least when vacuum states are allowed.
Abstract: It is shown that physical solutions of the Navier–Stokes equations for one-dimensional, compressible flow need not depend continuously on their initial data, at least when vacuum states are allowed. Specifically, two fluid regions initially separated by a third region of very low density 6 are considered. It is shown that, as $\delta \to 0$, the (unique) solutions corresponding to$\delta > 0$ do not in fact converge to a physical solution, but rather to a nonphysical weak solution in which the two fluids cannot collide, independent of their initial velocities, and whose separate momenta need not be conserved. A particular consequence is that solutions of the cavity problem $\delta = 0$ are not unique.

197 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated a simplified model of the Ericksen-Leslie system, which is a system of the Navier-Stokes equations coupled with the harmonic map flow.
Abstract: In the 1960s, Ericksen and Leslie established the hydrodynamic theory for modelling liquid crystal flow. In this paper, we investigate a simplified model of the Ericksen–Leslie system, which is a system of the Navier–Stokes equations coupled with the harmonic map flow. We prove global existence of solutions to the Ericksen–Leslie system in $${\mathbb{R}^{2}}$$ with initial data, where the solutions are regular except for at a finite number of singular times.

197 citations

Journal ArticleDOI
TL;DR: In this paper, a generalization of Bjorken flow is described, where the medium has finite transverse size and expands both radially and along the beam axis, and the local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.
Abstract: I explain a generalization of Bjorken flow where the medium has finite transverse size and expands both radially and along the beam axis. If one assumes that the equations of viscous hydrodynamics can be used, with p={epsilon}/3 and zero bulk viscosity, then the flow I describe can be developed into an exact solution of the relativistic Navier-Stokes equations. The local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.

197 citations

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations in dimension 2 were shown to be controllable in the case that the fluid is incompressible and slips on the boundary in agreement with Navier slip boundary conditions.
Abstract: For boundary or distributed controls, we get an approximate controllability result for the Navier-Stokes equations in dimension 2 in the case where the fluid is incompressible and slips on the boundary in agreement with the Navier slip boundary conditions.

197 citations

Journal ArticleDOI
R. T. Davis1
TL;DR: Viscous shock layer equations of laminar hypersonic flow past blunt body at moderate to high Reynolds numbers were given in this article, where the body was assumed to have a blunt body.
Abstract: Viscous shock layer equations of laminar hypersonic flow past blunt body at moderate to high Reynolds numbers

196 citations


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