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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 ${\rm Tr}A\equiv0$ …
Denis Serre's user avatar
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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.
Denis Serre's user avatar
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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 …
Denis Serre's user avatar
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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 …
Denis Serre's user avatar
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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 …
Denis Serre's user avatar
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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 …
Denis Serre's user avatar
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