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Results tagged with ap.analysis-of-pdes
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user 7089
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
4
votes
1
answer
719
views
Heuristic probabilistic argument for the Navier-Stokes existence and smoothness conjecture
The Collatz Conjecture is a famous conjecture that has never been proven; nevertheless, there exists a simple heuristic probabilistic argument which supports its truth - in Wikipedia's words, "If one …
- 2,649
3
votes
Heuristic probabilistic argument for the Navier-Stokes existence and smoothness conjecture
The following is the best probabilistic heuristic argument I know, which convinces me that either there is no blow up of the 3D Navier-Stokes equations for any initial data, or a blow up is very unlik …
- 2,649
2
votes
2
answers
437
views
2d incompressible Euler equations under periodic boundary conditions
It is well known that the 2d incompressible Navier-Stokes equations under periodic boundary conditions always have global smooth solutions, given smooth initial conditions.
I tried searching for a p …
- 2,649