Long-time behavior for 2D non-autonomous g-Navier-Stokes equations

Cung The Anh, and Dao Trong Quyet. "Long-time behavior for 2D non-autonomous g-Navier-Stokes equations." Annales Polonici Mathematici 103.3 (2012): 277-302. <http://eudml.org/doc/281024>.

@article{CungTheAnh2012,
abstract = {We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback $_σ$-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent and “small”, the existence, uniqueness and global stability of a stationary solution are also studied.},
author = {Cung The Anh, Dao Trong Quyet},
journal = {Annales Polonici Mathematici},
keywords = {-Navier-Stokes equation; weak solution; Galerkin method; pullback attractor; fractal dimension; stationary solution; global stability},
language = {eng},
number = {3},
pages = {277-302},
title = {Long-time behavior for 2D non-autonomous g-Navier-Stokes equations},
url = {http://eudml.org/doc/281024},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Cung The Anh
AU - Dao Trong Quyet
TI - Long-time behavior for 2D non-autonomous g-Navier-Stokes equations
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 3
SP - 277
EP - 302
AB - We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback $_σ$-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent and “small”, the existence, uniqueness and global stability of a stationary solution are also studied.
LA - eng
KW - -Navier-Stokes equation; weak solution; Galerkin method; pullback attractor; fractal dimension; stationary solution; global stability
UR - http://eudml.org/doc/281024
ER -