{\mathscr{N}}(u)\right\}  +
     \left(
       \begin{array}{c}
        G_1(t)-\nu (v^1_{x_3}+v^3_{x_1}) \\
          G_2(t)-\nu (v^2_{x_3}+v^3_{x_2})\\
       \end{array}
     \right),$$ where $K={\rm diag}\, (k_1, k_2)$ and $${\mathscr{N}}(u)\equiv \left(
    \begin{aligned}
        N_{11} & \; N_{12} \\
        N_{12} &\; N_{22}
    \end{aligned}
\right)= {\mathscr{C}}(\epsilon_0 ({\bar{u}})+ w K + f(\nabla w))$$ with ${\bar{u}}=(u_1;u_2)$, ${\mathscr{C}}(\epsilon)=2(1-\mu)^{-1}\left[\mu \, {\rm trace}\, \epsilon \cdot  I +(1-\mu)\epsilon \right]$ and $$\epsilon_0({\bar{u}})=\frac 12 (\nabla {\bar{u}}+ \nabla ^T {\bar{u}}),
\quad f(s)=\frac 12 s \otimes s, \; s\in {{\mathbb R}}^2.$$ This form of the full von Karman system was used earlier by many authors in the case when the fluid velocity field $v$ is absent and $k_i\equiv 0$ (see, e. g., [@puel-AMO96] or [@KochLa_2002] and the references therein).

Our main goal in this paper is to prove well-posedness of the problem in – in the class of finite energy solutions (see Theorem \[th:WP\]) and to show a possibility of compact long-time dynamics (see Theorem \[th:attractor\] on the existence of a compact global attractor). We note for the proof of uniqueness in Theorem \[th:WP\] relies substantially on the $H^1$-regularity of $w_t$, which follows from the structure of the mass operator $M_{{\alpha}}$ and involves Sedenko’s method (see [@Sed91b; @Sed_1997]). To prove the existence of a global attractor in Theorem \[th:attractor\] we use J.Ball’s method (see [@ball] 