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A Open problems in PDE research

  1. Mar 10, 2016 #1
    Hi everyone. For people who already saw me in this forum, I know I may seem boring with all these questions about PDE, but I promise this will be the last :D
    Anyway, as the title says, which are the main trends of differential equations research, especially nonlinear differential equations(which are widely used in cancer research, just to mention an example)?
    Secondly, are those problems most related with finding a particular solution for a differential equation, or are they concerned with the existence and regularity of solutions in a given domain?
  2. jcsd
  3. Mar 10, 2016 #2


    Staff: Mentor

    The major one is solving the Navier-Stokes PDE used in fluid mechanics:


    The Navier-Stokes problem is also a Millenium problem so there's big money behind the solution that you can give away to charity or just refuse like Russian mathematician Grigori Perelman did:


    and there's these problems from the unsolved list on wikipedia:

  4. Mar 10, 2016 #3
    I found Navier Stokes' equations interesting, mainly for the fact that, as far as I know, they've many implications in cancer modelling (Exchange between blood flow and tumor, and interactions between cancer and therapy). The problem is that I only managed to find millenium problems, which I couldn't be able to answer, neither now nor in the future. Are there any "simpler" problems related to Navier Stokes, and which are studied nowadays?
    P.S. Yes, I know about Perelman :) He lives with his mother now, or something like that :D
  5. Mar 11, 2016 #4
    anyone else?
  6. Mar 11, 2016 #5


    Staff: Mentor

  7. Mar 11, 2016 #6
    Thanks a lot!
    And what about nonlinearity, instead? I guess there's some research going in that direction as well...
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