Neel Patel


I am interested in analysis, especially partial differential equations. I passed my qualifying exam with major topic PDE/harmonic analysis and minor topic algebraic number theory. I have worked in kinetic theory and am now also interested in fluid dynamics.


  1. N. Patel and R. Strain, Large Time Decay Estimates for the Muskat Equation, arXiv:1610.05271
  2. N. Patel, Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System, arXiv:1607.07416
  3. Peter S. Landweber, Emanuel A. Lazar and Neel Patel, On Fiber Diameters of Continuous Maps, The American Mathematical Monthly, Vol. 123, No. 4 (April 2016), pp. 392-397

Qualifying Exam Notes

Below are some notes I wrote up to study for a qualifying exam in PDE/analysis. My references included Grafakos' Classical Fourier Analysis , Evans' Partial Differential Equations , Folland's Introduction to Partial Differential Equations , and Fourier Analysis and Nonlinear Partial Differential Equations by Bahouri-Chemin-Danchin in addition to notes from class. Please note that there are mistakes in the notes! I have not edited these notes.
Exam Notes Part 1 Exam Notes Part 2 Exam Notes Part 3