The generalized complex Ginzburg-Landau (CGL) equation describes the evolution of a
complex-valued field u= u (x, t) by Əru= Ru+(1+ iv)▲ u−(1+ iµ)| u| 2º u. It has a long history in …

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers
equation with small viscosity under periodic boundary conditions and to interpreting the …

Using weighted-norms we derive new bounds on the long-time behaviour of the solutions
improving on the known results of the polynomial growth with respect to the instability …

We consider non-linear Schrödinger equations with small complex coefficient of size δ in
front of the Laplacian. The space-variable belongs to the unit n-cube (n≤\bf3 and Dirichlet …

It is well known that the Euler equations in two spatial dimensions have global classical
solutions. We provide a new proof which is analytic rather than geometric. It is set in an …

In this paper, the authors have studied a generalized Ginzburg–Landau equation in two
spatial dimensions (2D). They have shown that this equation, under periodic boundary …

In this paper we study a complex derivative Ginzburg–Landau equation with two spatial
variables (2D). We obtain sufficient conditions for the existence and uniqueness of global …

This paper deals with the initial-boundary value problem (denoted by (CGL)) for the complex
Ginzburg–Landau type equation∂ u∂ t−(λ+ i α) Δ u+(κ+ i β)| u| q− 1 u− γ u= 0 with initial …

Two related open problems in the theory of 3 D Navier-Stokes turbulence are discussed in
this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation …

The diameter in the L∞-norm of the global attractor of the complex Ginzburg-Landau
equation ut=(1+ iα) Δu+ Ru−(1+ iβ) u2σu is estimated by using weighted energy estimates …