Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit
2021 ◽
Vol 240
(1)
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pp. 295-326
Keyword(s):
AbstractIn this paper we prove the uniform-in-time $$L^p$$ L p convergence in the inviscid limit of a family $$\omega ^\nu $$ ω ν of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution $$\omega $$ ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $$\omega ^{\nu }$$ ω ν to $$\omega $$ ω in $$L^p$$ L p . Finally, we show that solutions of the Euler equations with $$L^p$$ L p vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.
2013 ◽
Vol 14
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pp. 1-68
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Vol 107
(3)
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pp. 288-314
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2019 ◽
Vol 234
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pp. 727-775
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2010 ◽
Vol 63
(11)
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pp. 1469-1504
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2019 ◽
Vol 376
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pp. 353-384
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2012 ◽
Vol 316
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pp. 171-198
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2017 ◽
Vol 40
(14)
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pp. 5161-5176
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2010 ◽
Vol 8
(4)
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pp. 965-998
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