3 citations · 3 across the 7 of their papers we have counts for
8 papers
Global time-analytic strong solutions for a class of 3-wave kinetic equations
Nguyen Gia Hien, Gigliola Staffilani, Minh-Binh Tran
We study a class of 3-wave kinetic equations arising in wave turbulence theory, with regularized kernels. For radial, nonnegative initial data, we construct an exact global-in-time…
A Microlocal Open-Boundary Method for Residual-Based Wave Solvers on Unbounded Domains
Avy Soffer, Nguyen Gia Hien, Minh-Binh Tran
We introduce a microlocal phase-space-filtered physics-informed neural network (PINN--TDPSF or Microlocal PINNFilter) framework for wave propagation on unbounded domains. The metho…
Finite time energy cascade for mixed and wave kinetic equations
Gigliola Staffilani, Minh-Binh Tran
In this work we study a kinetic equation whose collision operator comprises three distinct wave interaction mechanisms: one representing a 3-wave process, and two corresponding to…
Evolution of finite temperature Bose-Einstein Condensates: Some rigorous studies on condensate growth
Gigliola Staffilani, Minh-Binh Tran
In trapped Bose-Einstein condensates (BECs), \emph{condensate growth} refers to the process in which an increasing number of quasi-particles are immediately transferred from the no…
Formation of condensations for non-radial solutions to 3-wave kinetic equations
Gigliola Staffilani, Minh-Binh Tran
We consider in this work a -dimensional -wave kinetic equation describing the dynamics of the thermal cloud outside a Bose-Einstein Condensate. We construct global non-radial…
Condensation and non-condensation times for 4-wave kinetic equations
Gigliola Staffilani, Minh-Binh Tran
Inspired by the pioneering work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under v…
On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations
Gigliola Staffilani, Minh-Binh Tran
Inspired by the fundamental work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under…
On the wave turbulence theory for a stochastic KdV type equation
Gigliola Staffilani, Minh-Binh Tran
Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We s…