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Potential Theory

  1. Dec 28, 2004 #1
    Dear friends,

    I need to know, in the theory of the potential, what must I do to study the caracteristics of this formulae:

    [tex]0=\vec{v} [\nabla \vec{j}+ \frac{ \partial \vec{D}}{\partial t} ]+ [\nabla \vec{D} \frac {\partial \vec{v}}{\partial t} ]+ \nabla \vec{D} (\vec{v} \nabla ) \vec{v}[/tex]

    Thanks you so much

    R. Aparicio.
     
  2. jcsd
  3. Dec 28, 2004 #2

    dextercioby

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    I'm not sure what u mean by "characteristics".If u mean the "characteristic curves" or "integral curves",then there is a problem as the equation u posted has 3 vector variables in 3D (probably),which means 9 unknowns.I'm absolutely sure that u couldn't find any integral curves...By the way,maybe if u told us where did u get this eq.and what [itex] \vec{D} [/itex] and [itex]\vec{j} [/itex] mean (i assumed \vec(v) was transport velocity),we could give you some more help...Mathematically speaking it is a quasilinear first order homogeneous PDE.As it's only one eq.and about 9 unknown functions,i'm sure it is part of a system of PDE-s.
    So,help us to help you... :smile:

    Daniel.
     
    Last edited: Dec 28, 2004
  4. Dec 29, 2004 #3
    Maxwell

    Dear Daniel,

    Is an ecuation that I have seen in a book, that is a part of a theory that says that the formula includes the 2 law of newton. It's a formula that could be a part of the system of formulas from Maxwell. My answer is that if there's a way to resolve it, or if could have information about what really means it.

    R.Aparicio.
     
  5. Dec 29, 2004 #4

    dextercioby

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    Yes,most of the fluid dynamics equations are derived from the second law of dynamics by Newton.However,a more riguros approach would involve Botzmann's equation.
    The only system of equations by Maxwell i know of is the one in electrodynamics.Your equation looks fluid dynamics to me.
    I already told u that it is a first order PDE with 9 unknowns and only one equation.It cannot be solved.You need exactly 9 INDEPENDENT equations to solve for each of the components of the 3 vectors.
    I cannot give you the signification,since you haven't revealed the context:the book/article/univ.course from where u've gotten it...

    Daniel.
     
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