caa a22 4500 605515697 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00205-015-0841-6 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0841-6 On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models [Elektronische Daten] [Nathan Glatt-Holtz, Vladimír Šverák, Vlad Vicol] 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. Springer-Verlag Berlin Heidelberg, 2015 Glatt-Holtz Nathan Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA aut Šverák Vladimír Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut Vicol Vlad Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 619-649 0003-9527 217:2<619 2015 217 205 https://doi.org/10.1007/s00205-015-0841-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0841-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Glatt-Holtz Nathan Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA aut NATIONALLICENCE 700 1- Šverák Vladimír Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 700 1- Vicol Vlad Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 619-649 0003-9527 217:2<619 2015 217 205