The importance of Luis Caffarelli's work in the study of fluids

Abstract

In this paper we describe the work of Luis Caffarelli in the area of fluid mechanics and related topics. Not only has his work on fluid mechanics been very influential, but many of his contributions that do not directly relate to fluid mechanics, such as his important results on the fractional Laplacian or the regularity of solutions to linear parabolic equations with oscillating coefficients, have been used in the study of fluids in many important ways. Thus, any review of his work has to include his contributions to the general (partial) regularity theory of solutions of Navier-Stokes equations and other studies related to fluid motion.

References in corpus (12)

• An extension problem related to the fractional Laplacian
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Nonlinear porous medium flow with fractional potential pressure
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Global regularity for a modified critical dissipative quasi-geostrophic equation
• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
• Eventual regularization for the slightly supercritical quasi-geostrophic equation
• Absence of anomalous dissipation of energy in forced two dimensional fluid equations
• Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations
• An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data
• Localized smoothing for the Navier-Stokes equations and concentration of critical norms near singularities
• Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness