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Results tagged with fluid-dynamics
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user 12120
2
votes
Steady Euler flows with compact support?
According to the following paper, it is an open problem whether such solutions exist:
N. Nadirashvili, Liouville theorem for Beltrami flow, Geometric and Functional Analysis 24 (2014), 916-921.
- 13k
12
votes
Convergence of solutions to Navier-Stokes to Euler's equation for viscosity $\to$ zero
There is a rather extensive literature on this, starting with the following paper of Kato:
T. Kato, Remarks on zero viscosity limit for nonstationary Navier-Stokes flows
with boundary, In: Seminar on …
- 13k
1
vote
PDE involving curl
This is an example of a first order system. A necessary condition for well-posedness of initial value problems is hyperbolicity. But even if F is the identity, the simplest case, this system is not hy …
- 13k
1
vote
Domain of the Stokes operator
If $\Omega$ has reentrant corners, then solutions of the Stokes problem will in general have corner singularities which prevent $H^2$ regularity. Therefore, if you define the Stokes operator in the ma …
- 13k