Applications of Bourgain-Brézis inequalities to fluid mechanics and magnetism

DOI10.1016/j.crma.2015.10.005zbMath1338.35325arXiv1509.01472OpenAlexW2160423919MaRDI QIDQ282707

Sagun Chanillo, Po-Lam Yung, Jean Van Schaftingen

Publication date: 12 May 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01472

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (3)

The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity ⋮ Approximation in higher-order Sobolev spaces and Hodge systems ⋮ Bourgain-Brezis inequalities on symmetric spaces of non-compact type

Cites Work

• Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem
• New estimates for elliptic equations and Hodge type systems
• Two-dimensional Navier-Stokes flow with measures as initial vorticity
• The Navier-Stokes equation for an incompressible fluid in \(\mathbb{R}^ 2\) with a measure as the initial vorticity
• Global solutions of two-dimensional Navier-Stokes and Euler equations
• Remarks on the preceding paper by M. Ben-Artzi ``Global solutions of two- dimensional Navier-Stokes and Euler equations
• New estimates for the Laplacian, the div-curl, and related Hodge systems
• Estimates for \(L^{1}\)-vector fields
• An Improved Strichartz Estimate for Systems with Divergence Free Data

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