12 papers · 1 filter
The energy of fractional Allen--Cahn layers in dimension one
Alvaro Carballeira, Damien Galant, Javier Gómez-Serrano
We study the energy of the one-dimensional fractional Allen--Cahn layer solution , defined as the unique odd, increasing solution of $(-Δ)^{s} Φ…
Linear instability of a Burgers--Hilbert traveling wave
Ãngel Castro, Javier Gómez-Serrano, Miguel M. G. Pascual-Caballo
We study the stability of traveling wave solutions to the Burgers--Hilbert equation on in the regime of small frequency and large wave speed . For and…
Nested nodal loops of biharmonic functions
Javier Gómez-Serrano, Robert Koirala, Alexander Logunov
Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meani…
Homogeneous steady states for the generalized surface quasi-geostrophic equations
Ken Abe, Javier Gómez-Serrano, In-Jee Jeong
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant , representing the 2D…
Discovery of Unstable Singularities
Yongji Wang, Mehdi Bennani, James Martens +19
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Eul…
Quasiperiodic solutions of the generalized SQG equation
Javier Gómez-Serrano, Alexandru D. Ionescu, Jaemin Park
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an e…