Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published March 15, 2016 | Submitted
Report Open

On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations


We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundary of a cylindrical domain. We prove the local well-posedness of the model in spaces of zero-mean functions, and study the potential formation of a finite-time singularity under certain convexity conditions for the velocity field. It is hoped that the results obtained on the 1D model will be useful in the analysis of the full 3D problem, whose loss of regularity in finite time has been observed in a recent numerical study (Luo and Hou, 2013).

Additional Information

Submitted on 13 Nov 2013. This work was supported in part by NSF FRG Grant DMS-1159138.

Attached Files

Submitted - 1311.2613.pdf


Files (256.0 kB)
Name Size Download all
256.0 kB Preview Download

Additional details

August 19, 2023
October 18, 2023