This short note serves as an introduction to the papers [35, 36]. These two works deal with the existence of mild solutions on the one hand and local energy weak solutions on the other hand to the Navier-Stokes equations in the half-space . We emphasize a concentration result for (sub)critical norms near a potential singularity. The contents of these notes were presented during the X-EDP seminar at IHÉS in October 2017.
@article{SLSEDP_2017-2018____A2_0, author = {Christophe Prange}, title = {Infinite energy solutions to the {Navier-Stokes} equations in the half-space and applications}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:2}, pages = {1--18}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2017-2018}, doi = {10.5802/slsedp.114}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.114/} }
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Christophe Prange. Infinite energy solutions to the Navier-Stokes equations in the half-space and applications. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 2, 18 p. doi : 10.5802/slsedp.114. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.114/
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