Nondispersive decay for the cubic wave equation

Nondispersive Solutions to the L-critical Half-wave Equation

We consider the focusing L2-critical half-wave equation in one space dimension i∂tu = Du− |u|u, where D denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold M∗ > 0 such that all H1/2 solutions with ‖u‖L2 < M∗ extend globally in time, while solutions with ‖u‖L2 > M∗ may develop singularities in finite time. In this paper, we first prove the ex...

Weighted energy decay for 3D wave equation

We obtain a dispersive long-time decay in weighted energy norms for solutions to the 1D wave equation with generic potential. The decay extends the results obtained by Murata for the 1D Schrödinger equation.

Universality of global dynamics for the cubic wave equation

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behaviour at the threshold of blowup. Mathematics Subject Classificatio...

Global Infinite Energy Solutions for the Cubic Wave Equation

— 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 probability measures.

Decay Estimates for the Wave Equation with Potential*