Self-similar Solutions of the Cubic Wave Equation

Autor:	Bizoń, P., Breitenlohner, P., Maison, D., Wasserman, A.
Rok vydání:	2009
Předmět:	Mathematics - Analysis of PDEs General Relativity and Quantum Cosmology
Zdroj:	Nonlinearity 23:225-236,2010
Druh dokumentu:	Working Paper
DOI:	10.1088/0951-7715/23/2/002
Popis:	We prove that the focusing cubic wave equation in three spatial dimensions has a countable family of self-similar solutions which are smooth inside the past light cone of the singularity. These solutions are labeled by an integer index $n$ which counts the number of oscillations of the solution. The linearized operator around the $n$-th solution is shown to have $n+1$ negative eigenvalues (one of which corresponds to the gauge mode) which implies that all $n>0$ solutions are unstable. It is also shown that all $n>0$ solutions have a singularity outside the past light cone which casts doubt on whether these solutions may participate in the Cauchy evolution, even for non-generic initial data. Comment: 14 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0905.3834 Zobrazit plný text záznamu View this record from Arxiv