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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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TL;DR: In this article, the authors prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω).
Abstract: We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear “ 21 2 - dimensional ” limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.
179 citations
TL;DR: In this article, two-dimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundary-layer flow.
Abstract: Two-dimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundary-layer flow. In the presen ...
179 citations
TL;DR: In this paper, a new numerical method for solving the incompressible, unsteady Navier?Stokes equations in vorticity?velocity formulation is presented, based on a compactdifference discretization of the streamwise and wall-normal derivatives in Cartesian coordinates.
179 citations
TL;DR: In this paper, the authors derived a detailed, pointwise description of the Green's function for this system, which generalizes the notion of diffusion wave introduced by Liu in the one-dimensional case, being expressible as a nonstandard heat kernel convected by the hyperbolic solution operator of the linearized compressible Euler equations.
Abstract: In [2], we determined a unique "effective artificial viscosity" system approximating the behavior of the compressible Navier-Stokes equations. Here, we derive a detailed, pointwise description of the Green's function for this system. This Green's function generalizes the notion of "diffusion wave" introduced by Liu in the one-dimensional case, being expressible as a nonstandard heat kernel convected by the hyperbolic solution operator of the linearized compressible Euler equations. It dominates the asymptotic behavior of solutions of the (nonlinear) compressible Navier-Stokes equations with localized initial data. The problem reduces to determining estimates on the wave equation, with initial data consisting of various combinations of heat and Riesz kernels; however, the calculations turn out to be surprisingly subtle, involving cancellation not captured by standard \(L^p\) estimates for the wave equation.
178 citations
TL;DR: The numerical scheme used by the present time-accurate FEM numerical method for incompressible Navier-Stokes equations, using primitive variables as the unknowns, is a Crank-Nicholson implicit treatment of all equation terms with central differencing for space derivatives as discussed by the authors.
178 citations