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© 2002-2007 Prof. Dr. Hans Wilhelm Alt, University of Bonn, Germany

Exercise 8 (Differential equation of stream functions)

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Differential equation of stream functions    [aufgabe:8]
  • [aufgabe:8-(a)] Seien  v ,  ψ  wie in Aufgabe 3 a). Nimm an, dass  v  durch
    v=a(∇ϕ + g)
    gegeben ist, wobei  a>0 ,  ϕ∈C2(Ω)  und  g∈C1(Ω;R2)  ist. Zeige, dass  ψ  die Differentialgleichung
    div (
    1
    a
    		 ∇ψ-i g)=0
    erfüllt.
  • [aufgabe:8-(b)] Seien  q ,  ψ  wie in Aufgabe aufgabe:3-(b). Nimm an, dass  v  der Gleichung
    q=- a (∇p+γ ez)
    genügt, wobei  a, γ>0  und  p∈C2(Ω)  ist. Zeige, dass für  ψ  die Differentialgleichung
    div (
    1
    r a
    		 ∇ψ+γer)=0
    erfüllt ist.
Version 1.5
H.W. Alt - 02.01.2007

Exercise 7 (Stream function) Exercise 7 (Stream function)
Exercises Exercises
Exercise 9 (Weak derivative) Exercise 9 (Weak derivative)
Exercise 9 (Weak derivative) Index
© 2002-2007 Prof. Dr. Hans Wilhelm Alt, University of Bonn, Germany