Regularity for Solutions to the Navier-Stokes Equations with one Velocity Component Regular
| dc.contributor.author | He, Cheng | |
| dc.date.accessioned | 2020-07-31T20:38:44Z | |
| dc.date.available | 2020-07-31T20:38:44Z | |
| dc.date.issued | 2002-03-17 | |
| dc.description.abstract | In this paper, we establish a regularity criterion for solutions to the Navier-stokes equations, which is only related to one component of the velocity field. Let (u, p) be a weak solution to the Navier-Stokes equations. We show that if any one component of the velocity field u, for example u3, satisfies either u3 ∈ L∞ (ℝ3 x (0, T)) or ∇u3 ∈ Lp(0, T; Lq(ℝ3)) with 1/p + 3/2q = 1/2 and q ≥ 3 for some T > 0, then u is regular on [0, T]. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | He, C. (2002). Regularity for solutions to the Navier-Stokes equations with one velocity component regular. <i>Electronic Journal of Differential Equations, 2002</i>(29), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12277 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Navier-Stokes equations | |
| dc.subject | Weak solutions | |
| dc.subject | Regularity | |
| dc.title | Regularity for Solutions to the Navier-Stokes Equations with one Velocity Component Regular | |
| dc.type | Article |