1. ## Well-posed Schrödinger equation

hi,
i need to find non trivial conditions, for which the following system is well posed.
and then prove it is well posed.

$
u_{t}=\imath [A_{1}u_{xx} + A_{2}u_{yy}] \ + \ B_{1}u_{x}+B_{2}u_{y} \ +\ Cu \ +\ F \
$

$
u(t=0,x)=f(x);\ f(x)=f(x+2\pi) \
$

$
u\in C^N; \ A_j,B_j,C_j\in C^N; \ A_j=A_j^*; \ j=1,2
$

2. the conditions should be on B obiuosly.
but i dont know of what kind, and how to prove it is well posed

i dont must use the optimal B, but i need one that would be easy to prove
i guess that taking B to be unitare ( B=B*), will solve it, but i'm not sure