Thread: how to solve du/dt = rot(u)

1. how to solve du/dt = rot(u)

hi, im trying to solve this pde:
Find $u:R^3 \times R^+ \rightarrow R^3$ that satyfies
$\\ \begin{cases} \frac{\partial u}{\partial t} = rot(u) \\ u(\bold{x},0)=\bold{v}*\cos(\alpha x + \beta y + \gamma z) \end{cases}$
where
$\\ \bold{x}=(x,y,z) \\ \bold{v} \in R^3 \\ \alpha, \beta, \gamma \in R$
Can anyone help me please? I have the exam tuesday

2. Re: how to solve du/dt = rot(u)

it's ok, i found the solution
$u(x,t)=\frac{\bold{v}}{2}(e^{P(i\bold{\omega})t}e^ {i\bold{\omega}\cdot \bold{x}}+e^{P(-i\bold{\omega})}e^{-i\bold{\omega}\cdot \bold{x}})$
with $\omega=(\alpha, \beta, \gamma)$ and $P(i\omega)$ the symbol of rot