### Abstract

We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable x. Assuming that dim = 4, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schrödinger equation.

Original language | English |
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Pages (from-to) | 3805-3822 |

Number of pages | 18 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 12 |

DOIs | |

Publication status | Published - 26 Mar 2004 |

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### Cite this

*Journal of Physics A: Mathematical and General*,

*37*(12), 3805-3822. https://doi.org/10.1088/0305-4470/37/12/006

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*Journal of Physics A: Mathematical and General*, vol. 37, no. 12, pp. 3805-3822. https://doi.org/10.1088/0305-4470/37/12/006

**Randomly forced CGL equation : Stationary measures and the inviscid limit.** / Kuksin, Sergei; Shirikyan, Armen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Randomly forced CGL equation

T2 - Stationary measures and the inviscid limit

AU - Kuksin, Sergei

AU - Shirikyan, Armen

PY - 2004/3/26

Y1 - 2004/3/26

N2 - We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable x. Assuming that dim = 4, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schrödinger equation.

AB - We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable x. Assuming that dim = 4, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schrödinger equation.

UR - http://www.scopus.com/inward/record.url?scp=1842683021&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/12/006

DO - 10.1088/0305-4470/37/12/006

M3 - Article

VL - 37

SP - 3805

EP - 3822

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 12

ER -