On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models
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| 024 | 7 | 0 | |a 10.1007/s00205-015-0841-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0841-6 | ||
| 245 | 0 | 0 | |a On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models |h [Elektronische Daten] |c [Nathan Glatt-Holtz, Vladimír Šverák, Vlad Vicol] |
| 520 | 3 | |a We study inviscid limits of invariant measures for the 2D stochastic Navier-Stokes equations. As shown by Kuksin (J Stat Phys 115(1-2):469-492, 2004), the noise scaling $${\sqrt{\nu}}$$ ν is the only one which leads to non-trivial limiting measures, which are invariant for the 2D Euler equations. Using a Moser-type iteration for stochastic drift-diffusion equations, we show that any limiting measure $${\mu_{0}}$$ μ 0 is in fact supported on bounded vorticities. Relationships of $${\mu_{0}}$$ μ 0 to the long term dynamics of 2D Euler in $${L^{\infty}}$$ L ∞ with the weak* topology are discussed. We also obtain a drift-independent modulus of continuity for a stationary deterministic model problem, which leads us to conjecture that in fact $${\mu_0}$$ μ 0 is supported on $${C^0}$$ C 0 . Moreover, in view of the Batchelor-Krainchnan 2D turbulence theory, we consider inviscid limits for a weakly damped stochastic Navier-Stokes equation. In this setting we show that only an order zero noise scaling (with respect to ν) leads to a nontrivial limiting measure in the inviscid limit. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Glatt-Holtz |D Nathan |u Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA |4 aut | |
| 700 | 1 | |a Šverák |D Vladimír |u Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA |4 aut | |
| 700 | 1 | |a Vicol |D Vlad |u Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 619-649 |x 0003-9527 |q 217:2<619 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0841-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0841-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Glatt-Holtz |D Nathan |u Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Šverák |D Vladimír |u Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Vicol |D Vlad |u Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 619-649 |x 0003-9527 |q 217:2<619 |1 2015 |2 217 |o 205 | ||