Applications of Bourgain-Brézis inequalities to fluid mechanics and magnetism

Sagun Chanillo; Jean Van Schaftingen; Po Lam Yung

doi:10.1016/j.crma.2015.10.005

Applications of Bourgain-Brézis inequalities to fluid mechanics and magnetism

Sagun Chanillo, Jean Van Schaftingen, Po Lam Yung

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	51-55
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	1
DOIs	https://doi.org/10.1016/j.crma.2015.10.005
Publication status	Published - 1 Jan 2016
Externally published	Yes

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10.1016/j.crma.2015.10.005

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title = "Applications of Bourgain-Br{\'e}zis inequalities to fluid mechanics and magnetism",

abstract = "As a consequence of inequalities due to Bourgain-Br{\'e}zis, 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.",

author = "Sagun Chanillo and {Van Schaftingen}, Jean and Yung, {Po Lam}",

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AU - Chanillo, Sagun

AU - Van Schaftingen, Jean

AU - Yung, Po Lam

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N2 - 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.

AB - 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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U2 - 10.1016/j.crma.2015.10.005

DO - 10.1016/j.crma.2015.10.005

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EP - 55

JO - Comptes Rendus Mathematique

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IS - 1

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Applications of Bourgain-Brézis inequalities to fluid mechanics and magnetism

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