2 citations · 3 across the 7 of their papers we have counts for
8 papers
Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension
Siddhant Agrawal, Neel Patel
We consider the Hele-Shaw problem with surface tension in an infinite domain. We prove the existence of a family of self-similar solutions. At , these solutions have a corner…
Uniqueness of the 2D Euler equation on rough domains
Siddhant Agrawal, Andrea R. Nahmod
We consider the 2D incompressible Euler equation on a bounded simply connected domain . We give sufficient conditions on the domain so that for all initial vorticity $ω_0 \i…
Uniform in gravity estimates for 2D water waves
Siddhant Agrawal
We consider the 2D gravity water waves equation on an infinite domain. We prove a local wellposedness result which allows interfaces with corners and cusps as initial data and whic…
Refined Rellich boundary inequalities for the derivatives of a harmonic function
Siddhant Agrawal, Thomas Alazard
The classical Rellich inequalities imply that the -norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined…
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…
Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner
Siddhant Agrawal, Andrea R. Nahmod
We consider the 2D incompressible Euler equation on a corner domain with angle with . We prove that if the initial vorticity $ω_0 \in L^{1}(Ω)\cap L^{\inf…
Angled crested like water waves with surface tension II: Zero surface tension limit
Siddhant Agrawal
This is the second paper in a series of papers analyzing angled crested type water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume t…
Rigidity of singularities of 2D gravity water waves
Siddhant Agrawal
We consider the Cauchy problem for the 2D gravity water wave equation. Recently Wu \cite{Wu15, Wu18} proved the local well-posedness of the equation in a regime which allows interf…