REVIEW 2 cited by
Global dissipative solutions of the 3D Naiver-Stokes and MHD equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
For any divergence free initial data in $H^\frac12$, we prove the existence of infinitely many dissipative solutions to both the 3D Navier-Stokes and MHD equations, whose energy profiles are continuous and decreasing on $[0,\infty)$. If the initial data is only $L^2$, our construction yields infinitely many solutions with continuous energy, but not necessarily decreasing. Our theorem does not hold in the case of zero viscosity as this would violate the weak-strong uniqueness principle due to Lions. This was achieved by designing a convex integration scheme that takes advantage of the dissipative term.
Forward citations
Cited by 2 Pith papers
-
Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces
Uniqueness of mild Navier–Stokes solutions in critical Besov spaces holds exactly for p<n (any q) or p=n (q≤2), and fails — even for zero initial data — for p=n, q>2 and for p>n.
-
Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations
Weak solutions of the Euler and Navier-Stokes equations exist for which two different particle trajectories start from the same point, in sharp regularity ranges, both with and without Brownian noise.
Discussion (0). Continue with ORCID to comment.