Optimal bounds for the inviscid limit of Navier–Stokes equations
By Hammadi Abidi, Raphaël Danchin. Asymptotic Analysis, 2004
49 citations recorded by the source corpus.
We consider the inviscid limit of incompressible two‐dimensional fluids with initial vorticity in L∞ and in some Besov space Bη2,∞ with low regularity index. We obtain a general result of strong convergence in L2 which applies to the case of vortex patches with smooth boundaries. The rate of convergence we find is (νt)3/4 (where ν stands for the viscosity and t, for the time). It improves the (νt)1/2 rate given by P. Constantin and J. Wu in (Nonlinearity 8 (1995), 735–742). Besides, it is shown to be optimal in the case of circular vortex patches.
Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/57b016d5addd73f2ad8b01296c5c776183c6e973
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In Applied Mathematics
- Peter Constantin
- Yasunori Maekawa
- Nader Masmoudi
- Vlad Vicol
- Igor Kukavica
- Frédéric Rousset
- Luis Silvestre
- Alexis Vasseur
In Computational Mechanics
- Peter Constantin
- Yasunori Maekawa
- Nader Masmoudi
- Vlad Vicol
- Igor Kukavica
- Frédéric Rousset
- Fei Wang
- Davdi Gerard-Varet
In Control and Systems Engineering
Citations in the corpus
- On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane (2012, background): “[13, 49, 20, 6] for regular solutions, [32, 34, 10, 9, 11, 12, 33, 2, 18, 35, 14] for nonsmooth solutions including vortex patches or point vortices.”
- Remarks about the Inviscid Limit of the Navier–Stokes System (2007, methodology): “Here, we would like to extend the result of Abid and Danchin [1] to the 3D case and also give a slight improvement of their 2D result by allowing u0 − u0 to be just in L(2).”
- On the Euler equations of incompressible fluids (2007, background): “In some nonsmooth regimes (smooth vortex patches), the finite time inviscid limit exists and optimal rates of convergence for the velocity can be obtained ([1], [108]), but the rates (for the vorticity) deteriorate when the smoothness of the initial data deteriorates – for nonsmooth vortex patches (”