Timeline for How to tell, roughly, which PDE's are interesting to analyse?
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14 events
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| May 18, 2020 at 19:58 | comment | added | Mark | David, in addition to all the answers here, if you have time to spend check out the book: Polyanin, Zaitsev - Handbook of Nonlinear Partial Differential Equations, 2008. You have a few thousand PDEs there and you maybe find some of them interesting to analyze. | |
| Mar 28, 2020 at 17:07 | history | became hot network question | |||
| Mar 28, 2020 at 16:18 | comment | added | David | Dear Igor, actually, what I can see is that PDE research for beginners usually begins with a specific problem being chosen for them, and they learn tools to solve it and then move on to (usually only modestly) more difficult but somewhat similar specific problems. In this way they branch out a little bit, but how far they branch out depends on the individual. I was trying to get at understanding what's beyond this, or maybe how to pick my own problems. | |
| Mar 28, 2020 at 9:41 | comment | added | Igor Khavkine | I will echo the answer by Denis Serre. In mathematical, and related theoretical work, one often finds two different situations: "problems in search of solutions" and "solutions in search of problems". If you have some independent motivation for studying a PDE, that is your problem and you need to solve it, which is pretty self-explanatory. By your question, you're probably not in this first situation. On the other hand, if you set yourself the task to study a certain method or technique (a "solution"), then some PDEs naturally manifest as relevant "problems". | |
| Mar 28, 2020 at 8:57 | answer | added | Denis Serre | timeline score: 6 | |
| Mar 28, 2020 at 5:02 | comment | added | Francois Ziegler | “Interesting” PDEs often have more geometrical (e.g. integral) formulations, whose analysis can feel different from “write an arbitrary PDO and crank in the Strichartz estimates”. | |
| Mar 28, 2020 at 4:30 | comment | added | user6976 | Navier–Stokes seems to be OK. | |
| Mar 28, 2020 at 4:30 | history | edited | David | CC BY-SA 4.0 |
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| Mar 28, 2020 at 3:57 | history | edited | David | CC BY-SA 4.0 |
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| Mar 28, 2020 at 3:43 | comment | added | Neal | A PDE is interesting to analyze if mathematicians are interested in its analysis. What kinds of PDEs are other folks in your field thinking about, and why do they find them interesting? | |
| Mar 28, 2020 at 3:36 | history | edited | David | CC BY-SA 4.0 |
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| Mar 28, 2020 at 3:30 | comment | added | Piyush Grover | PDEs can come from other sources than physics: geometry , stochastic processes and economics are examples of such fields. | |
| Mar 28, 2020 at 3:20 | review | First posts | |||
| Mar 28, 2020 at 3:44 | |||||
| Mar 28, 2020 at 3:18 | history | asked | David | CC BY-SA 4.0 |