Advances in Differential Equations

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

Vincent Masselin

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140391

Mathematical Reviews number (MathSciNet)
MR1850386

Zentralblatt MATH identifier
1022.35071

Subjects
Primary: 35Q58
Secondary: 35J60: Nonlinear elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

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.


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