Provided the initial velocity and the external body force are sufficiently smooth, there exist , and a unique continuous family of strong solutions () of the Euler or Navier–Stokes initial–boundary value problem on the time interval . The solutions of the Navier–Stokes problem satisfy a Navier-type boundary condition.
Pourvu que les données soient suffisamment régulières, il existe , et famille unique de solutions fortes, locales en temps sur et dépendant continûment de ν, pour les problèmes d'Euler ou de Navier–Stokes. Ces solutions vérifient des conditions aux limites de type celles de Navier.
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@article{CRMATH_2009__347_19-20_1141_0, author = {Bellout, Hamid and Neustupa, Ji\v{r}{\'\i} and Penel, Patrick}, title = {On viscosity-continuous solutions of the {Euler} and {Navier{\textendash}Stokes} equations with a {Navier-type} boundary condition}, journal = {Comptes Rendus. Math\'ematique}, pages = {1141--1146}, publisher = {Elsevier}, volume = {347}, number = {19-20}, year = {2009}, doi = {10.1016/j.crma.2009.09.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.09.007/} }
TY - JOUR AU - Bellout, Hamid AU - Neustupa, Jiří AU - Penel, Patrick TI - On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition JO - Comptes Rendus. Mathématique PY - 2009 SP - 1141 EP - 1146 VL - 347 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.09.007/ DO - 10.1016/j.crma.2009.09.007 LA - en ID - CRMATH_2009__347_19-20_1141_0 ER -
%0 Journal Article %A Bellout, Hamid %A Neustupa, Jiří %A Penel, Patrick %T On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition %J Comptes Rendus. Mathématique %D 2009 %P 1141-1146 %V 347 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.09.007/ %R 10.1016/j.crma.2009.09.007 %G en %F CRMATH_2009__347_19-20_1141_0
Bellout, Hamid; Neustupa, Jiří; Penel, Patrick. On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1141-1146. doi : 10.1016/j.crma.2009.09.007. http://www.numdam.org/articles/10.1016/j.crma.2009.09.007/
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