In this work we show that, in the class of L∞((0,T); L2(T3)) distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in some open interval of times are meagre in the sense of Baire category, and the Leray ones are a nowhere dense set.
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DOI : 10.1051/cocv/2022038
Keywords: Iincompressible Navier-Stokes equations, nonsmooth distributional solutions, Leray solutions, convex integration, Baire category
@article{COCV_2022__28_1_A38_0,
author = {Colombo, Maria and De Rosa, Luigi and Sorella, Massimo},
title = {Typicality results for weak solutions of the incompressible {Navier{\textendash}Stokes} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022038},
mrnumber = {4438714},
zbl = {1492.35181},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022038/}
}
TY - JOUR AU - Colombo, Maria AU - De Rosa, Luigi AU - Sorella, Massimo TI - Typicality results for weak solutions of the incompressible Navier–Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022038/ DO - 10.1051/cocv/2022038 LA - en ID - COCV_2022__28_1_A38_0 ER -
%0 Journal Article %A Colombo, Maria %A De Rosa, Luigi %A Sorella, Massimo %T Typicality results for weak solutions of the incompressible Navier–Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022038/ %R 10.1051/cocv/2022038 %G en %F COCV_2022__28_1_A38_0
Colombo, Maria; De Rosa, Luigi; Sorella, Massimo. Typicality results for weak solutions of the incompressible Navier–Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 38. doi: 10.1051/cocv/2022038
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