On partial regularity of steady-state solutions to the 6D Navier-Stokes equations

On partial regularity of steady-state solutions to the 6D Navier-Stokes equations. Dong, H. & Strain, R. M. Indiana Univ. Math. J., 61(6):2211–2229, 2012.

Arxiv

On partial regularity of steady-state solutions to the 6D Navier-Stokes equations [pdf]

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Consider steady-state weak solutions to the incompressible Navier-Stokes equations in six spatial dimensions. We prove that the 2D Hausdorff measure of the set of singular points is equal to zero. This problem was mentioned in 1988 by Struwe, during his study of the five dimensional case.

@article{MR3129108,
	abstract = {Consider steady-state weak solutions to the incompressible
Navier-Stokes equations in six spatial dimensions. We prove that the 2D
Hausdorff measure of the set of singular points is equal to zero.  This problem was mentioned in 1988 by Struwe, during his study of the five dimensional case.},
	author = {Dong, Hongjie and Strain, Robert M.},
	date-added = {2019-07-13 15:27:26 -0400},
	date-modified = {2019-07-13 15:27:26 -0400},
	doi = {10.1512/iumj.2012.61.4765},
	eprint = {1101.5580},
	fjournal = {Indiana University Mathematics Journal},
	issn = {0022-2518},
	journal = {Indiana Univ. Math. J.},
	keywords = {Navier-Stokes equations, Fluid mechanics},
	mrclass = {35Q30 (35B65 76D03 76D05)},
	mrnumber = {3129108},
	mrreviewer = {Kazuo Yamazaki},
	number = {6},
	pages = {2211--2229},
	title = {On partial regularity of steady-state solutions to the 6{D} {N}avier-{S}tokes equations},
	url_arxiv = {https://arxiv.org/abs/1101.5580},
	url_pdf = {https://strain.math.upenn.edu/preprints/ds6DssNSE.pdf},
	volume = {61},
	year = {2012},
	zblnumber = {1286.35193},
	bdsk-url-1 = {https://doi.org/10.1512/iumj.2012.61.4765}}

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