Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

Hao Jia; Vladimír Šverák

doi:10.1007/s00222-013-0468-x

Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

School of Mathematics

Research output: Contribution to journal › Article › peer-review

124 Scopus citations

Abstract

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

Original language	English (US)
Pages (from-to)	233-265
Number of pages	33
Journal	Inventiones Mathematicae
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s00222-013-0468-x
State	Published - Apr 2014

Bibliographical note

Funding Information:
This work was supported in part by grant DMS 1101428 from the National Science Foundation.

Publisher link

10.1007/s00222-013-0468-x

Find It

Find It at U of M Libraries

Cite this

@article{947b6b896e084a728168aaca11be9b06,

title = "Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions",

abstract = "We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.",

author = "Hao Jia and Vladim{\'i}r {\v S}ver{\'a}k",

note = "Funding Information: This work was supported in part by grant DMS 1101428 from the National Science Foundation. ",

year = "2014",

month = apr,

doi = "10.1007/s00222-013-0468-x",

language = "English (US)",

volume = "196",

pages = "233--265",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

AU - Jia, Hao

AU - Šverák, Vladimír

N1 - Funding Information: This work was supported in part by grant DMS 1101428 from the National Science Foundation.

PY - 2014/4

Y1 - 2014/4

N2 - We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

AB - We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

UR - https://www.scopus.com/pages/publications/84896388252

UR - https://www.scopus.com/pages/publications/84896388252#tab=citedBy

U2 - 10.1007/s00222-013-0468-x

DO - 10.1007/s00222-013-0468-x

M3 - Article

AN - SCOPUS:84896388252

SN - 0020-9910

VL - 196

SP - 233

EP - 265

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 1

ER -

Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this