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Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains
Global attractor for a Klein-Gordon-Schrodinger type system
| 1. | Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Greece |
| 2. | Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Hellas, Greece |
$i\psi_t + k\psi_(xx) + i\alpha\psi$ = $\phi\psi + f(x)$,
$\phi_(tt)$ - $\phi_(xx) + \phi + \lambda\phi_t$ = -$Re\psi_x + g(x)$,
$\psi(x,0)=\psi_0(x), \phi(x,0)$ = $\phi_0, \phi_t(x,0)=\phi_1(x)$
$\phi(x,t)=\phi(x,t)=0$, $x\in\partial\Omega, t>0$
where $x \in \Omega, t > 0, k > 0, \alpha > 0, \lambda > 0, f(x)$ and $g(x)$ are the driving terms and $\Omega$ (bounded) $\subset \mathbb{R}$. Also we prove the continuous dependence of solutions of the system on the initial data as well as the existence of a global attractor.
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