## Differential and Integral Equations

- Differential Integral Equations
- Volume 24, Number 3/4 (2011), 231-260.

### Dynamics of stochastic Klein--Gordon--Schrödinger equations in unbounded domains

Boling Guo, Yan Lv, and Xiaoping Yang

#### Abstract

The long-time behavior in the
sense of distributions for stochastic
Klein--Gordon--Schrödinger equations in the whole space ${\mathbb
R}^n$, $1\leq n\leq 3$, is
studied. First the existence of one stationary
measure from any
moment-finite initial data in the space $H^1({\mathbb
R}^n)\times H^1({\mathbb R}^n) \times
L^2({\mathbb R}^n)$ is proved and then
a global measure attractor is
constructed in the space consisting of
probability measures
supported on $H^2({\mathbb R}^n)\times H^2({\mathbb
R}^n)\times H^1({\mathbb R}^n)$.
Because of the
lack of compact
embedding, some *a priori* estimates and a
split of solutions play
important roles in the approach.

#### Article information

**Source**

Differential Integral Equations, Volume 24, Number 3/4 (2011), 231-260.

**Dates**

First available in Project Euclid: 20 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356019032

**Mathematical Reviews number (MathSciNet)**

MR2757459

**Zentralblatt MATH identifier**

1240.60187

**Subjects**

Primary: 60F10: Large deviations 60H15: Stochastic partial differential equations [See also 35R60] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

#### Citation

Lv, Yan; Guo, Boling; Yang, Xiaoping. Dynamics of stochastic Klein--Gordon--Schrödinger equations in unbounded domains. Differential Integral Equations 24 (2011), no. 3/4, 231--260. https://projecteuclid.org/euclid.die/1356019032