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Results tagged with fluid-dynamics
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user 8799
16
votes
Convergence of solutions to Navier-Stokes to Euler's equation for viscosity $\to$ zero
To complete Michael's answer, the only situation that is under control is that of the Cauchy problem: the spatial domain is ${\mathbb R}^d$ or ${\mathbb T}^d$ (case of periodic solutions). This means …
- 52.3k
3
votes
Surjectivity of curl
I think that the answer is Yes.
1st step. Because Fourier transform is an automorphism of the Schwartz class, the problem is equivalent to show that every vector field $v(x)\in{\mathcal S}({\mathbb R …
- 52.3k
1
vote
Pressureless explicit solutions to incompressible Euler
Partial answer.
If you assume in addition that the solution is classical ('smooth'), then the Jacobian $A(t)$ of the velocity field along a trajectory ('characteristics') satisfies ${\rm Tr}A\equiv0$ …
- 52.3k
2
votes
Navier-Stokes fluid dynamics, Einstein gravity and holography
This is a bit too long for being a comment.
An important remark is that the NS equation is parabolic and therefore the velocity at which information propagates is unbounded. For instance, if the init …
- 52.3k
7
votes
Compressible Ebin-Marsden?
I have worked for decades on compressible gas dynamics, and I am not aware of such a followup by Ebin & Marsden. But I think you will find something in the book of Arnol'd & Khesin.
- 52.3k
10
votes
Accepted
Explanation for why an ideal fluid doesn't have increasing entropy?
This is a very important issue, to which an answer must be made in mathematical terms, rather than by waving hands.
Yes, the Euler system (conservation of mass, momentum and energy) is time-reversible …
- 52.3k