Asymptotic dynamics in double-diffusive convection

Mikołaj Piniewski. "Asymptotic dynamics in double-diffusive convection." Applicationes Mathematicae 35.2 (2008): 223-245. <http://eudml.org/doc/279962>.

@article{MikołajPiniewski2008,
abstract = {We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class $([0,∞); H) ∩ L²_\{loc\}(ℝ^+;V)$. This theorem enables us to show that the infinite-dimensional dynamical system generated by the double-diffusive convection equations has a global attractor on which the long-term dynamics of solutions is focused.},
author = {Mikołaj Piniewski},
journal = {Applicationes Mathematicae},
keywords = {thermohaline convection; existence; uniqueness; continuous dependence; long-term dynamics},
language = {eng},
number = {2},
pages = {223-245},
title = {Asymptotic dynamics in double-diffusive convection},
url = {http://eudml.org/doc/279962},
volume = {35},
year = {2008},
}

TY - JOUR
AU - Mikołaj Piniewski
TI - Asymptotic dynamics in double-diffusive convection
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 2
SP - 223
EP - 245
AB - We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class $([0,∞); H) ∩ L²_{loc}(ℝ^+;V)$. This theorem enables us to show that the infinite-dimensional dynamical system generated by the double-diffusive convection equations has a global attractor on which the long-term dynamics of solutions is focused.
LA - eng
KW - thermohaline convection; existence; uniqueness; continuous dependence; long-term dynamics
UR - http://eudml.org/doc/279962
ER -