Euler Equations, Navier-Stokes Equations and Turbulence

By Peter Constantin. 2006

208 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/442c1efae61209042d0a8e953f77ab66866196db

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation (2006, background): “ANNALS OF MATHEMATICS anmaah SECOND SERIES, VOL. 171, NO. 3 May, 2010 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation By Luis A. Caffarelli and Alexis Vasseur Annals of Mathematics, 171 (2010), 1903–1930 Drift diffusion equations with fractional diffusion and…”
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian (2007, background): “1 Introduction Constrained variational problems with fractional diffusion appear in the study of the quasi-geostrophic flow model [8,9], anomalous diffusion [3] and American options with jump processes [10] (see also [16]).”
Convex integration and phenomenologies in turbulence (2019, background): “For a detailed study of turbulence theories we refer the reader to the books [6, 149, 150, 81, 79, 194], the surveys papers with a mathematical perspective [32, 66, 165, 33, 71, 180, 5, 69], and to the references therein.”
Nonlocal elliptic equations in bounded domains: a survey (2015, background): “In applications, this type of nonlocal problems appear in models involving “anomalous diffusions” (in which the underlying stochastic process is not given by Brownian motion), or in the presence of long-range interactions or forces.”
Lp-maximal regularity of nonlocal parabolic equations and applications (2013, unknown): “In recent years there is great interest to study the above nonlocal equation, since it has appeared in numerous disciplines, such as quasi-geostrophic ﬂuid dynamics (cf. [10,9]), stochastic control problems (cf. [ 34]), non-linear ﬁltering with jump (cf .”
Euler equations for incompressible ideal fluids (2007, background): “The reader is referred, for instance, to the book of Majda and Bertozzi [50] and the recent review of Constantin [ 14 ] for addition relevant material.”
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem (2018, unknown): “Just to cite a few we refer to [16, 17, 19, 22, 27, 44] for some physical models, [1, 23, 34] for some applications in finances, [13] for applications in fluid dynamics, [21, 26, 32] for application in ecology and [20] for some applications in image processing.”
On the Euler equations of incompressible fluids (2007, methodology): “The conservation of circulation follows from the Weber formula (see ([40], [42]) and references therein)”
Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces (2006, background): “This identity allowed him to obtain a calculus inequality involving fractional derivatives [7].”