### Existence of a solution for a system related to the singularity for the 3D Zakharov system

Vincent Masselin

#### Abstract

We prove the existence of infinitely many radial solutions for a system of equations in $\mathbb R^3$. Numerically, that is supposed to give the profile of an asymptotic self-similar blow-up solution of the Zakharov system in dimension three. For this, we use several techniques of ordinary differential equations and especially a kind of shooting method. Moreover, we give some properties of solutions, monotonicity, estimates at infinity and integral relations.

#### Article information

Source
Adv. Differential Equations, Volume 6, Number 10 (2001), 1153-1172.

Dates
First available in Project Euclid: 2 January 2013

Mathematical Reviews number (MathSciNet)
MR1850386

Zentralblatt MATH identifier
1022.35071

#### Citation

Masselin, Vincent. Existence of a solution for a system related to the singularity for the 3D Zakharov system. Adv. Differential Equations 6 (2001), no. 10, 1153--1172. https://projecteuclid.org/euclid.ade/1357140391