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What is the basis of PDEs?

  1. Jul 24, 2013 #1
    Is there a hole in knowledge as to the origins of PDEs?

    If there is a void, is Schwartz space a suitable basis?

    Schwartz spaces are intermediate between general spaces and nuclear spaces.
    Infra-Schwartz spaces are intermediate between Schwartz spaces and reflexive spaces.
     
    Last edited: Jul 24, 2013
  2. jcsd
  3. Jul 25, 2013 #2
    I learned all about Schwartz space in a book called Nuclear and Conuclear Spaces, Herni Hogbe-Nlend, Chapter 1.
     
  4. Jul 25, 2013 #3

    HallsofIvy

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    I don't understand what you mean by the "basis" or "origins" of PDEs. What, exactly are you looking for?
     
  5. Jul 25, 2013 #4
    PDEs model physical systems.
    All systems are subjected to nonlinear turbulence.
    I am wondering if Schwartz space is suitable for modeling general PDEs.
     
  6. Jul 25, 2013 #5

    MarneMath

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    I would wager the general answer is no since a Schwartz space requires a special property of a function's derivative that not all functions may have. If you're asking can you use a Schwartz space for some PDE's, the answer is yes.
     
  7. Jul 25, 2013 #6
    Do you know if Schwartz space fits the Navier-Stokes equations?
     
    Last edited: Jul 25, 2013
  8. Jul 25, 2013 #7

    MarneMath

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    I'm not an expert regarding PDE's or methods dealing with them, so I don't want to give you a wrong answer but I'll give a minimum answer that you probably know if you are asking these questions. I don't believe Navier-Stokes must be in a Schwartz Space unless the initial data is a Schwartz Class. So with that said if you want to look at the N-S equation via a Schwartz Class you can do so. You can probably even extract that information to gather information on global properties for initial Schwartz Class data.
     
  9. Jul 25, 2013 #8

    MarneMath

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    I have no idea what you're trying to get at besides advertising for a book and author.
     
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