# Asymptotic dynamics in double-diffusive convection

Applicationes Mathematicae (2008)

- Volume: 35, Issue: 2, page 223-245
- ISSN: 1233-7234

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topMikołaj 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 -

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