In this paper we consider the long time behavior of solutions of a version of gKdV equation
on the real line. The existence of the global attractor in H2 (R) is proved when the force f …

Abstract We consider the Navier–Stokes equation (NS) in dimensions two and three as limits
of the fractional approximations. In 2-D the NS problem is critical with respect to the standard …

The generalized KdV–Burgers equation [Formula: see text], δ, ν> 0, γ≥ 0, is considered in
this paper. Using the parabolic regularization technique we prove local and global …

In this paper, we study the long time behavior of solutions to a weakly dissipative fractional
Korteweg de Vries (KdV) equation on the real line R. The main difficulty lies in that the …

In this work, we are interested in the finite fractal dimensionality of the global attractor for a
weakly damped Kordeweg‐de Vries (KdV) equation. For the KdV equation with periodic …

Cauchy's problem for a generalization of the KdV–Burgers equation is considered in
Sobolev spaces H^ 1 (R) and H^ 2 (R). We study its local and global solvability and the …

We prove the existence of the global attractor in-method to the damped and forced mKdV,
because the Miura transformation does not work for the mKdV with damping and forcing …

In this paper, we study the long-time behavior of solutions to the generalized Korteweg–de
Vries–Burgers equation of the form We prove the existence of pullback attractors Aν in H1 …

We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial
non-linearity, damping, and forcing that matches the smoothing level for the gKdV at $ H …

We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial
non-linearity, damping, and forcing that matches the smoothing level for the gKdV at H1. As …