## Research

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.

## Publications

- N. Patel and R. Strain,
*Large Time Decay Estimates for the Muskat Equation*, arXiv:1610.05271 - N. Patel,
*Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System*, arXiv:1607.07416 - 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

*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.