3,469 karma · joined February 28, 2013
This is wrong. We already know that these equations do not model correctly the real world. No model correctly models the real world and every model breaks down eventually at one point or another. Showing that a certain set of equations leads to non-unique results under certain conditions means nothing, unless you also show that those ‘certain conditions’ are true in cases where we previously assumed the model to hold. If you only show that in cases where we previously also assumed the equations not to hold, they actually output nonsense, this may be a mathematically curious and nice result but of no physical relevance.
So far, this result looks more like realising that Newton’s gravitational field diverges for a point particle of nonzero mass, which is not really any indication whatsoever that it doesn’t correctly model the real world.
Contrary to what the article claims here:
> the exact same fluid from the exact same starting conditions could end up in two distinct physical states, which makes no physical sense
it makes quite a lot of "physical sense" to get two possible outcomes out of one initial state, though we would not expect the Navier-Stokes equations to describe that situation.
The article is simply wrong in arguing that because we expect classical fluids to behave classically and because Navier-Stokes may break down in certain limits, NS may be a bad model. I actually struggle to put together a coherent sentence which comes close to what the article tries to say regarding the relation between "physical sense" and our expectations for the results of Navier-Stokes.
Unfortunately closed-source (though open for collaborations), otherwise there’d be a link here.
So far, this approach has paid of tremendously both for me as well as my supervisor, as the reuse value is quite high and performance very competitive, resulting in many projects both within the former chair and also with external collaborations.
Could you clarify why you think that this site does not require a valid license to re-host and re-compile papers?
I also don’t want to keep tabs on every arXiv rehoster and inform them manually by e-mail every time a new paper goes up.
May I ask why this was not done together with the arXiv itself? I.e. have the infrastructure run there, let authors check the HTML render at the same time as the PDF render and then, if the author thinks they look ok, have them show directly on the abstracts page? This would even avoid all your license problems, as the arXiv already has the corresponding license!
Edit to clarify: If people want to use or develop a broken sort-of-PDF viewer, that’s fine. However, if someone searches for a paper of mine, I would like them to only find the version where I at least had a chance to see that it renders correctly and is complete. In particular, I do not want to be "responsible" for broken rendering on random third-party websites. This website actually operating illegally does not make me more inclined to support it.
If you don’t limit mitigation to "a config setting" (and why would you?!), a patch/new version is the best mitigation you can get.