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.
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.
Accepted:
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Sagun Chanillo 1; Jean Van Schaftingen 2; Po-Lam Yung 3
@article{CRMATH_2016__354_1_51_0, author = {Sagun Chanillo and Jean Van Schaftingen and Po-Lam Yung}, 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}, }
TY - JOUR AU - Sagun Chanillo AU - Jean Van Schaftingen AU - Po-Lam Yung 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 DO - 10.1016/j.crma.2015.10.005 LA - en ID - CRMATH_2016__354_1_51_0 ER -
Sagun Chanillo; Jean Van Schaftingen; Po-Lam Yung. Applications of Bourgain–Brézis inequalities to fluid mechanics and magnetism. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 51-55. doi : 10.1016/j.crma.2015.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.005/
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☆ 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.
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