50 citations · 83 across the 8 of their papers we have counts for
9 papers
Rigidity of Acute Angled Corners for One Phase Muskat Interfaces
Siddhant Agrawal, Neel Patel, Sijue Wu
We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. We prove local well-posedness for fluid interfaces that are g…
Well-posedness for SQG sharp fronts with unbounded curvature
Francisco Gancedo, Huy Q. Nguyen, Neel Patel
Patch solutions for the surface quasigeostrophic (SQG) equation model sharp temperature fronts in atmospheric and oceanic flows. We establish local well-posedness for SQG sharp fro…
Global Results for the Inhomogeneous Muskat Problem
Neel Patel, Nikhil Shankar
The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a non-uniform porous medium. We consider the case of a p…
Global Regularity for Gravity Unstable Muskat Bubbles
Francisco Gancedo, Eduardo Garcia-Juarez, Neel Patel +1
In this paper, we study the dynamics of fluids in porous media governed by Darcy's law: the Muskat problem. We consider the setting of two immiscible fluids of different densities…
On the local existence and blow-up for generalized SQG patches
Francisco Gancedo, Neel Patel
We study patch solutions of a family of transport equations given by a parameter , , with the cases and corresponding to the Euler and the surface quasi-geos…
On The Muskat Problem With Viscosity Jump: Global In Time Results
Francisco Gancedo, Eduardo Garcia-Juarez, Neel Patel +1
The Muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media. In this paper, we consider both the 2D and 3D setting…
Large Time Decay Estimates for the Muskat Equation
Neel Patel, Robert M. Strain
We prove time decay of solutions to the Muskat equation in 2D and in 3D. In \cite{JEMS} and \cite{CCGRPS}, the authors introduce the norms $\|f\|_{s}(t)= \int_{\mathbb{R}^{2}} |ξ|^…
Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System
Neel Patel
In this paper, we consider sufficient conditions, called continuation criteria, for global existence and uniqueness of classical solutions to the three-dimensional relativistic Vla…
On fiber diameters of continuous maps
Peter S. Landweber, Emanuel A. Lazar, Neel Patel
We present a surprisingly short proof that for any continuous map , if , then there exists no bound on the diameter of fibers of …