Editing Newton's laws of motion (section)

=== Singularities ===
It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time.<ref>{{Cite journal|last1=Saari|first1=Donald G.|author-link=Donald G. Saari|last2=Xia|first2=Zhihong|author-link2=Zhihong Xia|date=May 1995|title=Off to infinity in finite time|url=http://www.ams.org/notices/199505/saari-2.pdf|journal=[[Notices of the American Mathematical Society]]|volume=42|pages=538–546}}</ref> This unphysical behavior, known as a "noncollision singularity",<ref name="Barrow-Green2008" /> depends upon the masses being pointlike and able to approach one another arbitrarily closely, as well as the lack of a [[speed of light|relativistic speed limit]] in Newtonian physics.<ref>{{cite book|first=John C. |last=Baez |author-link=John C. Baez |chapter=Struggles with the Continuum |arxiv=1609.01421 |title=New Spaces in Physics: Formal and Conceptual Reflections |editor-first1=Mathieu |editor-last1=Anel |editor-first2=Gabriel |editor-last2=Catren |publisher=Cambridge University Press |year=2021 |isbn=978-1-108-49062-7 |oclc=1195899886 |pages=281–326}}</ref>

It is not yet known whether or not the Euler and Navier–Stokes equations exhibit the analogous behavior of initially smooth solutions "blowing up" in finite time. The question of [[Navier–Stokes existence and smoothness|existence and smoothness of Navier–Stokes solutions]] is one of the [[Millennium Prize Problems]].<ref>{{cite book|last1=Fefferman |first1=Charles L. |author-link1=Charles Fefferman |chapter=Existence and smoothness of the Navier–Stokes equation |url=https://www.claymath.org/sites/default/files/navierstokes.pdf |pages=57–67 |editor1-last=Carlson |editor1-first=James |editor2-last=Jaffe |editor2-first=Arthur |editor2-link=Arthur Jaffe |editor3-last=Wiles |editor3-first=Andrew |editor3-link=Andrew Wiles |title=The Millennium Prize Problems |year=2006 |location=Providence, RI |publisher=American Mathematical Society and Clay Mathematics Institute |isbn=978-0-821-83679-8 |oclc=466500872}}</ref>