5 papers
Dirac measures can be quantum limits on the Sierpinski gasket
Patricia Alonso Ruiz, Nikolay Tzvetkov
We prove that on the Sierpinski gasket, a prototype of compact fractal space, Dirac distributions arise as the weak limit of probability measures associated with sequences of high…
Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the ball
Nicolas Burq, Nicolas Camps, Chenmin Sun +1
We construct probabilistic strong solutions to the cubic Schrödinger equation on the three-dimensional ball with radial initial data, which is a significant improvement of a result…
On low regularity well-posedness of the binormal flow
Valeria Banica, Renato Lucà, Nikolay Tzvetkov +1
We focus on a class of solutions of the binormal flow, model of the evolution of vortex filaments, that generate several corner singularities in finite time. This phenomenon has be…
Global infinite energy solutions for the cubic wave equation
Nicolas Burq, Laurent Thomann, Nikolay Tzvetkov
We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probabil…
A simple criterion of transverse linear instability for solitary waves
F. Rousset, N. Tzvetkov
We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various exa…