[Applications des inégalités de Bourgain–Brézis à la mécanique des fluides et au magnétisme]
À partir d'inégalités de Bourgain–Brézis, nous démontrons le caractère bien posé localement dans le temps des équations de Navier–Stokes avec vitesse bornée en espace-temps et un tourbillon initial à variation bornée. Nous obtenons également des estimations en espace-temps pour le champ magnétique grâce à des inégalités de Strichartz améliorées.
As a consequence of inequalities due to Bourgain–Brézis, we obtain local-in-time well-posedness for the two-dimensional Navier–Stokes equation with velocity bounded in spacetime and initial vorticity in bounded variation. We also obtain spacetime estimates for the magnetic field vector through improved Strichartz inequalities.
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@article{CRMATH_2016__354_1_51_0,
author = {Chanillo, Sagun and Van Schaftingen, Jean and Yung, Po-Lam},
title = {Applications of {Bourgain{\textendash}Br\'ezis} inequalities to fluid mechanics and magnetism},
journal = {Comptes Rendus. Math\'ematique},
pages = {51--55},
publisher = {Elsevier},
volume = {354},
number = {1},
year = {2016},
doi = {10.1016/j.crma.2015.10.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.10.005/}
}
TY - JOUR AU - Chanillo, Sagun AU - Van Schaftingen, Jean AU - Yung, Po-Lam TI - Applications of Bourgain–Brézis inequalities to fluid mechanics and magnetism JO - Comptes Rendus. Mathématique PY - 2016 SP - 51 EP - 55 VL - 354 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.10.005/ DO - 10.1016/j.crma.2015.10.005 LA - en ID - CRMATH_2016__354_1_51_0 ER -
%0 Journal Article %A Chanillo, Sagun %A Van Schaftingen, Jean %A Yung, Po-Lam %T Applications of Bourgain–Brézis inequalities to fluid mechanics and magnetism %J Comptes Rendus. Mathématique %D 2016 %P 51-55 %V 354 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.10.005/ %R 10.1016/j.crma.2015.10.005 %G en %F CRMATH_2016__354_1_51_0
Chanillo, Sagun; Van Schaftingen, Jean; Yung, Po-Lam. Applications of Bourgain–Brézis inequalities to fluid mechanics and magnetism. Comptes Rendus. Mathématique, Tome 354 (2016) no. 1, pp. 51-55. doi : 10.1016/j.crma.2015.10.005. http://www.numdam.org/articles/10.1016/j.crma.2015.10.005/
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Cité par Sources :
☆ S.C. was partially supported by NSF grant DMS 1201474. J.V.S. was partially supported by the Fonds de la recherche scientifique, FNRS grant J.044.13. P.-L.Y. was partially supported by a direct grant for research from the Chinese University of Hong Kong (4053120). We thank Haïm Brézis for several comments that improved the paper.
