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What is De Giorgi Method in Fluid Dynamics about?
This document summarizes the De Giorgi method for proving regularity of solutions to nonlinear elliptic partial differential equations. It discusses how De Giorgi proved that solutions are continuous even when the coefficients are discontinuous, by using an iterative argument based on the interplay between Sobolev inequalities and energy inequalities. The method has since been applied successfully to problems in fluid dynamics like the Navier-Stokes and quasigeostrophic equations. The notes then provide an
- Author
- KM Hui
- Language
- EN