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
SN - 1361-6447
VL - 37
SP - 3805
EP - 3822
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 12
ER -