語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Low Regularity Solutions for Gravity...
~
Ai, Albert Lee.
FindBook
Google Book
Amazon
博客來
Low Regularity Solutions for Gravity Water Waves.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Low Regularity Solutions for Gravity Water Waves./
作者:
Ai, Albert Lee.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:
139 p.
附註:
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:
Dissertations Abstracts International81-04B.
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13886050
ISBN:
9781085792189
Low Regularity Solutions for Gravity Water Waves.
Ai, Albert Lee.
Low Regularity Solutions for Gravity Water Waves.
- Ann Arbor : ProQuest Dissertations & Theses, 2019 - 139 p.
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Thesis (Ph.D.)--University of California, Berkeley, 2019.
This item must not be sold to any third party vendors.
The gravity water waves equations are a system of partial differential equations which govern the evolution of the interface between a vacuum and an incompressible, irrotational fluid in the presence of gravity. In the case of two dimensions, these equations model non-breaking waves at the surface of a body of water, such as a lake or ocean, while in one dimension, they model non-breaking waves propagating in a channel.We are concerned with the well-posedness of the Cauchy problem for the gravity water waves equations: We seek to show that given an initial configuration of the vacuum-fluid interface and an initial fluid velocity field beneath the interface, there is a unique solution to the gravity water waves equations which matches the given initial data. In particular, we are concerned with the situation where the initial data has low regularity, corresponding to surface waves which are not necessarily smooth.The classical regularity threshold for the well-posedness of the water waves system requires initial velocity field in Hs, with s > d/2 + 1, and can be obtained by proving standard energy conservation estimates. On the other hand, it has been shown that for dispersive equations (equations describing phenomena which disperse waves of different frequencies), one can lower well-posedness regularity thresholds below that which is attainable by energy conservation alone. This was first realized for the nonlinear wave equation via dispersive estimates known as Strichartz estimates, and was first applied toward the well-posedness of gravity water waves by Alazard-Burq-Zuily.However, this approach was implemented as a partial result, using Strichartz estimates with loss relative to what one expects based on the corresponding linearized model problem. In this dissertation, we prove well-posedness with initial velocity field in Hs, s > d/2 + 1 - μ, where μ =1/10 in the case d = 1 and μ = 1/5 in the case d ≥ 2, extending the previous result of Alazard-Burq-Zuily. In the case of one dimension, using a further refined argument, we establish the well-posedness for s > 1/2 + 1 -1/8, corresponding to proving lossless Strichartz estimates. This provides the sharp regularity threshold with respect to the approach of combining Strichartz estimates with energy estimates.
ISBN: 9781085792189Subjects--Topical Terms:
515831
Mathematics.
Low Regularity Solutions for Gravity Water Waves.
LDR
:03268nmm a2200301 4500
001
2264277
005
20200423112940.5
008
220629s2019 ||||||||||||||||| ||eng d
020
$a
9781085792189
035
$a
(MiAaPQ)AAI13886050
035
$a
AAI13886050
040
$a
MiAaPQ
$c
MiAaPQ
100
1
$a
Ai, Albert Lee.
$3
3541382
245
1 0
$a
Low Regularity Solutions for Gravity Water Waves.
260
1
$a
Ann Arbor :
$b
ProQuest Dissertations & Theses,
$c
2019
300
$a
139 p.
500
$a
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500
$a
Advisor: Tataru, Daniel.
502
$a
Thesis (Ph.D.)--University of California, Berkeley, 2019.
506
$a
This item must not be sold to any third party vendors.
520
$a
The gravity water waves equations are a system of partial differential equations which govern the evolution of the interface between a vacuum and an incompressible, irrotational fluid in the presence of gravity. In the case of two dimensions, these equations model non-breaking waves at the surface of a body of water, such as a lake or ocean, while in one dimension, they model non-breaking waves propagating in a channel.We are concerned with the well-posedness of the Cauchy problem for the gravity water waves equations: We seek to show that given an initial configuration of the vacuum-fluid interface and an initial fluid velocity field beneath the interface, there is a unique solution to the gravity water waves equations which matches the given initial data. In particular, we are concerned with the situation where the initial data has low regularity, corresponding to surface waves which are not necessarily smooth.The classical regularity threshold for the well-posedness of the water waves system requires initial velocity field in Hs, with s > d/2 + 1, and can be obtained by proving standard energy conservation estimates. On the other hand, it has been shown that for dispersive equations (equations describing phenomena which disperse waves of different frequencies), one can lower well-posedness regularity thresholds below that which is attainable by energy conservation alone. This was first realized for the nonlinear wave equation via dispersive estimates known as Strichartz estimates, and was first applied toward the well-posedness of gravity water waves by Alazard-Burq-Zuily.However, this approach was implemented as a partial result, using Strichartz estimates with loss relative to what one expects based on the corresponding linearized model problem. In this dissertation, we prove well-posedness with initial velocity field in Hs, s > d/2 + 1 - μ, where μ =1/10 in the case d = 1 and μ = 1/5 in the case d ≥ 2, extending the previous result of Alazard-Burq-Zuily. In the case of one dimension, using a further refined argument, we establish the well-posedness for s > 1/2 + 1 -1/8, corresponding to proving lossless Strichartz estimates. This provides the sharp regularity threshold with respect to the approach of combining Strichartz estimates with energy estimates.
590
$a
School code: 0028.
650
4
$a
Mathematics.
$3
515831
650
4
$a
Fluid mechanics.
$3
528155
690
$a
0405
690
$a
0204
710
2
$a
University of California, Berkeley.
$b
Mathematics.
$3
1685396
773
0
$t
Dissertations Abstracts International
$g
81-04B.
790
$a
0028
791
$a
Ph.D.
792
$a
2019
793
$a
English
856
4 0
$u
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13886050
筆 0 讀者評論
館藏地:
全部
電子資源
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W9416511
電子資源
11.線上閱覽_V
電子書
EB
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入