Global solvability for double-diffusive convection system based on Brinkman-Forchheimer equation in general domains (Q315866)

The article generalizes previous results on the existence and uniqueness of solutions for the initial value problem of a double-diffusive convection system for a linearized Brinkman-Forchheimer equation from bounded to unbounded domains and for time-intervals of arbitrary length.NEWLINENEWLINEThe core of the proof consists of an application of Banach's fixed point theorem in order to obtain local-in-time solutions in appropriate Sobolev spaces.NEWLINENEWLINEThen, these solutions are extended to arbitrarily long time-intervals by establishing a priori estimates with the help of Gronwall's lemma.