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Up to the moment I am writing this question, I notice that there are only 98 questions for the tag. While there are 400 questions for the tag though, they are mainly about ordinary differential equations.

  • Does this fact suggest that people who ask questions in math.SE are less interested in PDE than other fields in mathematics?
  • Is it easy to be too localized for a PDE question so that people don't bother asking it here?
  • Will it be more appropriate to ask such questions in MO?
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    $\begingroup$ There is no correlation between subjects and appropriatedness for MO (apart from high school algebra and such...). The difference between the two sites is not thematical. $\endgroup$ – Mariano Suárez-Álvarez Sep 7 '11 at 3:07
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    $\begingroup$ As for your first question: doesn't it answer itself? $\endgroup$ – Mariano Suárez-Álvarez Sep 7 '11 at 3:08
  • $\begingroup$ @Mariano: OK. Admittedly, MO is more about the research level questions or the graduate level ones. But I don't understand why there are so few questions for this big branch in mathematics... Maybe the number of the questions for PDE in MO also answers the first question. $\endgroup$ – Jack Sep 7 '11 at 3:15
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    $\begingroup$ I should mention that it is true that there are more users (on MO, compared to Math.SE) whose names I recognize as someone working in PDEs or geometric analysis. However that doesn't mean more PDE questions are asked. The (ap.analysis-of-pdes) tag at MO has only around 250 questions, making it one tenth of (ag.algebraic-geometry) and (nt.number-theory), and less than one quarter of the more popular arXiv tags. So the relative numbers are not too different between MO and here. $\endgroup$ – Willie Wong Sep 7 '11 at 13:39
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    $\begingroup$ I would pay zero attention to the relative numbers. The askers here are mostly undergraduate students, so the frequencies reflect the popularity of a topic in undergrad programs (grad students ask less questions because they are outnumbered by undergrads and also are more familiar with other sources). If it makes you feel better I state that my favorite areas of finite fields, coding theory and Lie algebras have 56, 12 and 78 questions respectively. While that makes me a bit sad, it just shows that not even all graduate programs cover those topics. May be you are seeing the same phenomenon? $\endgroup$ – Jyrki Lahtonen Sep 8 '11 at 14:47
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  1. The answer is basically tautological: it indicates that people who ask questions on Math.SE are less likely to ask PDE questions.
  2. Not really. There is a lot of general theory of PDEs. And asking about specific equations can sometimes bring out illustrations of general techniques. (This is not just for PDEs, but also for group theory [applications of Sylow theorems], number theory [applications of Chinese remainder; quad. reciprocity], and practically all other fields of mathematics.) So closing a question as too localised because it is about a specific equation will just be absurd.
  3. Depends. Like Mariano says: MO is for research level questions. Some subjects are inherently better suited for MO by virtue of it being at the forefront of research (topos theory etc.), compared to subjects that have been so well studied that it is in the common curricula (single variable calculus). But for most subjects the distinction is whether the question arose from research or graduate (postgraduate in Brit-speak) activities.

Now, in regards to (3) above, the more theoretical aspects of PDEs are often only studied in graduate schools in North America. Very few undergraduate programs (that I know of) offer PDE courses beyond the method of characteristics for first order scalar equations and series/fundamental solutions of constant coefficient linear PDEs. So that sets the bar a bit high in the get-go.

Furthermore, the technical nature of the field means that researchers basically know everyone whose work is related to theirs, so, for example, in my case, if I have a question about a particular PDE that I am interested in, more often than not I will just fire off an e-mail to the two or three people I know who would have a chance at knowing the answer, instead of bothering to ask them on MO or MSE.

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    $\begingroup$ While it may be unnecessary to say that I'd still like to make the point: If you're unsure about posting here or on MO it may be better to post here first. If you don't get a good answer or helpful feedback within a reasonable amount of time (read: a few days, not a few hours) you can then go to MO with the safety-net of having asked here first. That worked well for many borderline questions. $\endgroup$ – t.b. Sep 7 '11 at 10:49
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    $\begingroup$ I forgot to mention it because it's so obvious: If you decide to move your question from here over to MO, please say that you asked here first and link to the original question. $\endgroup$ – t.b. Sep 7 '11 at 12:12
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For the sake of having an answer: your first question answers itself. I don't really understand the second question. Appropriateness for MO has nothing to do with subject (with the caveats noted by Mariano in the comments).

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