A blow-up criterion for the 3-D compressible Navier-Stokes equations

Dongfen Bian; Baoquan Yuan; Yue Hu

doi:10.1109/ICIST.2011.5765162

A blow-up criterion for the 3-D compressible Navier-Stokes equations

Dongfen Bian^*, Baoquan Yuan, Yue Hu

^*Corresponding author for this work

Henan Polytechnic University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, the blow-up criterion for the strong solutions to the compressible Navier-Stokes equations in ℝ³ is studied. We obtain that if sup_0≤t≤T ||ρ(t)||L^∞ + ||▽ρ(t)L_T^p(L^q(ℝ³)) + ∫₀^T || ▽u(t)||Ḃ _∞,∞⁰ dt < ∞, for 2/p + 3/q ≤ 2, 3 < q < ∞, then the strong solutions (ρ, u) can be continued beyond T.

Original language	English
Title of host publication	2011 International Conference on Information Science and Technology, ICIST 2011
Pages	1098-1102
Number of pages	5
DOIs	https://doi.org/10.1109/ICIST.2011.5765162
Publication status	Published - 2011
Externally published	Yes
Event	2011 International Conference on Information Science and Technology, ICIST 2011 - Nanjing, China Duration: 26 Mar 2011 → 28 Mar 2011

Publication series

Name	2011 International Conference on Information Science and Technology, ICIST 2011

Conference

Conference	2011 International Conference on Information Science and Technology, ICIST 2011
Country/Territory	China
City	Nanjing
Period	26/03/11 → 28/03/11

Access to Document

10.1109/ICIST.2011.5765162

Cite this

@inproceedings{da880699e03a46628abc68a556ade4ec,

title = "A blow-up criterion for the 3-D compressible Navier-Stokes equations",

abstract = "In this paper, the blow-up criterion for the strong solutions to the compressible Navier-Stokes equations in ℝ3 is studied. We obtain that if sup0≤t≤T ||ρ(t)||L∞ + ||▽ρ(t)LTp(Lq(ℝ3)) + ∫0T || ▽u(t)||Ḃ ∞,∞0 dt < ∞, for 2/p + 3/q ≤ 2, 3 < q < ∞, then the strong solutions (ρ, u) can be continued beyond T.",

author = "Dongfen Bian and Baoquan Yuan and Yue Hu",

year = "2011",

doi = "10.1109/ICIST.2011.5765162",

language = "English",

isbn = "9781424494408",

series = "2011 International Conference on Information Science and Technology, ICIST 2011",

pages = "1098--1102",

booktitle = "2011 International Conference on Information Science and Technology, ICIST 2011",

note = "2011 International Conference on Information Science and Technology, ICIST 2011 ; Conference date: 26-03-2011 Through 28-03-2011",

}

Bian, D, Yuan, B & Hu, Y 2011, A blow-up criterion for the 3-D compressible Navier-Stokes equations. in 2011 International Conference on Information Science and Technology, ICIST 2011., 5765162, 2011 International Conference on Information Science and Technology, ICIST 2011, pp. 1098-1102, 2011 International Conference on Information Science and Technology, ICIST 2011, Nanjing, China, 26/03/11. https://doi.org/10.1109/ICIST.2011.5765162

A blow-up criterion for the 3-D compressible Navier-Stokes equations. / Bian, Dongfen; Yuan, Baoquan; Hu, Yue.
2011 International Conference on Information Science and Technology, ICIST 2011. 2011. p. 1098-1102 5765162 (2011 International Conference on Information Science and Technology, ICIST 2011).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A blow-up criterion for the 3-D compressible Navier-Stokes equations

AU - Bian, Dongfen

AU - Yuan, Baoquan

AU - Hu, Yue

PY - 2011

Y1 - 2011

N2 - In this paper, the blow-up criterion for the strong solutions to the compressible Navier-Stokes equations in ℝ3 is studied. We obtain that if sup0≤t≤T ||ρ(t)||L∞ + ||▽ρ(t)LTp(Lq(ℝ3)) + ∫0T || ▽u(t)||Ḃ ∞,∞0 dt < ∞, for 2/p + 3/q ≤ 2, 3 < q < ∞, then the strong solutions (ρ, u) can be continued beyond T.

AB - In this paper, the blow-up criterion for the strong solutions to the compressible Navier-Stokes equations in ℝ3 is studied. We obtain that if sup0≤t≤T ||ρ(t)||L∞ + ||▽ρ(t)LTp(Lq(ℝ3)) + ∫0T || ▽u(t)||Ḃ ∞,∞0 dt < ∞, for 2/p + 3/q ≤ 2, 3 < q < ∞, then the strong solutions (ρ, u) can be continued beyond T.

UR - http://www.scopus.com/inward/record.url?scp=79957791664&partnerID=8YFLogxK

U2 - 10.1109/ICIST.2011.5765162

DO - 10.1109/ICIST.2011.5765162

M3 - Conference contribution

AN - SCOPUS:79957791664

SN - 9781424494408

T3 - 2011 International Conference on Information Science and Technology, ICIST 2011

SP - 1098

EP - 1102

BT - 2011 International Conference on Information Science and Technology, ICIST 2011

T2 - 2011 International Conference on Information Science and Technology, ICIST 2011

Y2 - 26 March 2011 through 28 March 2011

ER -

A blow-up criterion for the 3-D compressible Navier-Stokes equations

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this