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Angled crested like water waves with surface tension II : zero surface tension limit / by Siddhant Agrawal.
Math/Physics/Astronomy Library QA3 .A57 no.1458
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LIBRA QA3 .A57 no.1-no.154, no.156-no.228, no.230-no.236, no.238-no.289, no.291-no.312, no.314-no.334, no.336-no.338
Available from offsite location
Math/Physics/Astronomy Library QA3 .A57 no.313 (1984),no.335 (1985),no.339 (1986)-no.599 (1997) no.605 (1997)-no.860 (2006),no.865 (2006)-no.1243 (2019),no.1252 (2019)-no.1286 (2020),no.1288 (2020)-no.1385 (2022),no.1392 (2023)-no.1548 (2025),no.1554 (2025)-no.1620 (2026)
Mixed Availability
- Format:
- Book
- Author/Creator:
- Agrawal, Siddhant, author.
- Series:
- Memoirs of the American Mathematical Society ; 0065-9266 v. 1458.
- Memoirs of the American Mathematical Society, 0065-9266 ; no. 1458
- Language:
- English
- Subjects (All):
- Differential equations, Partial.
- Waves--Mathematical models.
- Waves.
- Physical Description:
- v, 124 pages : illustrations ; 26 cm.
- Place of Publication:
- Providence, RI : American Mathematical Society, [2024]
- Summary:
- This is the second paper in a series of papers analyzing angled crested like water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. In the first paper [1] we constructed a weighted energy which generalizes the energy of Kinsey and Wu [22] to the case of non-zero surface tension, and proved a local wellposedness result. In this paper we prove that under a suitable scaling regime, the zero surface tension limit of these solutions with surface tension are solutions to the gravity water wave equation which includes waves with angled crests.
- Contents:
- Chapter 1. Introduction
- Chapter 2. Notation and previous work from part 1 ; Notation ; The system ; Previous result
- Chapter 3. Main results and discussion ; Results ; Discussion
- Chapter 4. Identities and equations from previous work ; Main identities ; Quasilinear equations ; Previous a priori estimate
- Chapter 5. Higher order energy εhigh ; Quasilinear equation ; Quantities controlled by the energy of Ehigh ; Closing the energy estimate for Ehigh ; Equivalences of Ehigh and εhigh
- Chapter 6. Auxiliary energy εaux ; Quasilinear equation ; Quantities controlled by the energy λEaux ; Closing the energy estimate for λEaux ; Equivalence of λEaux and λεaux
- Chapter 7. The energy ε∆ ; Quantities controlled by E∆ ; Closing the energy estimate for E∆ ; Equivalence of E∆ and ε∆
- Chapter 8. Proof of Theorem 3.1.1 and Corollary 3.1.2
- Chapter 9. Appendix A
- Chapter 10. Appendix B
- Bibliography.
- Notes:
- "January 2024, volume 293, number 1458 (second of 7 numbers)."
- Includes bibliographical references (pages 123-124).
- ISBN:
- 1470467380
- 9781470467388
- OCLC:
- 1420334087
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