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Math Help - how to solve du/dt = rot(u)

  1. #1
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    Dec 2011
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    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
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  2. #2
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    Dec 2011
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    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
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