Existence and uniqueness of solutions to the Navier-Stokes equations in dimension two with forces in the space L$$((0, T); W$$(Ω)) for p and q in appropriate parameter ranges are proven. The case of spatially measured-valued forces is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions for any 1 < p, q < ∞.
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Keywords: Evolution Navier-Stokes equations, weak solutions, uniqueness clasess, sensitivity analysis, asymptotic stability
@article{COCV_2021__27_1_A63_0,
author = {Casas, Eduardo and Kunisch, Karl},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Well-posedness of evolutionary {Navier-Stokes} equations with forces of low regularity on two-dimensional domains},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021058},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021058/}
}
TY - JOUR AU - Casas, Eduardo AU - Kunisch, Karl ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021058/ DO - 10.1051/cocv/2021058 LA - en ID - COCV_2021__27_1_A63_0 ER -
%0 Journal Article %A Casas, Eduardo %A Kunisch, Karl %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021058/ %R 10.1051/cocv/2021058 %G en %F COCV_2021__27_1_A63_0
Casas, Eduardo; Kunisch, Karl. Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 61. doi: 10.1051/cocv/2021058
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Cité par Sources :
The first author was partially supported by Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P. The second was supported by the ERC advanced grant 668998 (OCLOC) under the EU’s H2020 research program.
