SMALL SCALES IN INVISCID LIMITS OF STEADY FLUIDS.
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| Title: | SMALL SCALES IN INVISCID LIMITS OF STEADY FLUIDS. |
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| Authors: | GUO, YAN1 yan_guo@brown.edu, YANG, ZHUOLUN2 yang.8242@osu.edu |
| Source: | SIAM Journal on Mathematical Analysis. 2025, Vol. 57 Issue 5, p5216-5242. 27p. |
| Subjects: | Navier-Stokes equations, Inviscid flow, Shear flow, Euler, Leonhard, 1707-1783, Boundary layer (Aerodynamics), Incompressible flow |
| Abstract: | In this article, we study the two-dimensional incompressible steady Navier-Stokes equation in a channel (- L, 0) × (- 1, 1) with the no-slip boundary condition on { Y = 土1 } and consider the inviscid limite ε→ 0. In the special case of Euler shear flow ( ue (Y), 0), we construct a steady Navier-Stokes solution for epsilon ε << 1, {uε ~ Ue+Up+O(√ε), &vε ~h(Y) exp{Xue(Y)/ε}+O√ε), where up represents the classical Prandtl layer profile, and h(Y) is an arbitrary smooth, compactly-supported function with small magnitude. While the classical Prandtl boundary layer up exhibits a small scale of order √ε in Y near Y = 土1 the profile we construct reveals an a small scale of Xue (Y) in the vertical velocity component. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 188483895 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: SMALL SCALES IN INVISCID LIMITS OF STEADY FLUIDS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22GUO%2C+YAN%22">GUO, YAN</searchLink><relatesTo>1</relatesTo><i> yan_guo@brown.edu</i><br /><searchLink fieldCode="AR" term="%22YANG%2C+ZHUOLUN%22">YANG, ZHUOLUN</searchLink><relatesTo>2</relatesTo><i> yang.8242@osu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Mathematical+Analysis%22">SIAM Journal on Mathematical Analysis</searchLink>. 2025, Vol. 57 Issue 5, p5216-5242. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Inviscid+flow%22">Inviscid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Shear+flow%22">Shear flow</searchLink><br /><searchLink fieldCode="DE" term="%22Euler%2C+Leonhard%2C+1707-1783%22">Euler, Leonhard, 1707-1783</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+layer+%28Aerodynamics%29%22">Boundary layer (Aerodynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Incompressible+flow%22">Incompressible flow</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, we study the two-dimensional incompressible steady Navier-Stokes equation in a channel (- L, 0) × (- 1, 1) with the no-slip boundary condition on { Y = 土1 } and consider the inviscid limite ε→ 0. In the special case of Euler shear flow ( ue (Y), 0), we construct a steady Navier-Stokes solution for epsilon ε << 1, {uε ~ Ue+Up+O(√ε), &vε ~h(Y) exp{Xue(Y)/ε}+O√ε), where up represents the classical Prandtl layer profile, and h(Y) is an arbitrary smooth, compactly-supported function with small magnitude. While the classical Prandtl boundary layer up exhibits a small scale of order √ε in Y near Y = 土1 the profile we construct reveals an a small scale of Xue (Y) in the vertical velocity component. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/24M1693726 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 5216 Subjects: – SubjectFull: Navier-Stokes equations Type: general – SubjectFull: Inviscid flow Type: general – SubjectFull: Shear flow Type: general – SubjectFull: Euler, Leonhard, 1707-1783 Type: general – SubjectFull: Boundary layer (Aerodynamics) Type: general – SubjectFull: Incompressible flow Type: general Titles: – TitleFull: SMALL SCALES IN INVISCID LIMITS OF STEADY FLUIDS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: GUO, YAN – PersonEntity: Name: NameFull: YANG, ZHUOLUN IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00361410 Numbering: – Type: volume Value: 57 – Type: issue Value: 5 Titles: – TitleFull: SIAM Journal on Mathematical Analysis Type: main |
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