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On Dispersive Effects In Inviscid Fl...

Widmayer, Klaus.

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On Dispersive Effects In Inviscid Fluids And Non-Uniqueness Of Weak Wave Maps.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On Dispersive Effects In Inviscid Fluids And Non-Uniqueness Of Weak Wave Maps./
作者:	Widmayer, Klaus.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	190 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-01(E), Section: B.
Contained By:	Dissertation Abstracts International78-01B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10139562
ISBN:	9781339950471

On Dispersive Effects In Inviscid Fluids And Non-Uniqueness Of Weak Wave Maps.
Widmayer, Klaus.

On Dispersive Effects In Inviscid Fluids And Non-Uniqueness Of Weak Wave Maps. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 190 p.

Source: Dissertation Abstracts International, Volume: 78-01(E), Section: B.

Thesis (Ph.D.)--New York University, 2016.

This work is devoted to the study of some aspects of the well-posedness theory of evolution differential equations in mathematical physics.

ISBN: 9781339950471Subjects--Topical Terms:

515831
Mathematics.

On Dispersive Effects In Inviscid Fluids And Non-Uniqueness Of Weak Wave Maps.
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500 $a Source: Dissertation Abstracts International, Volume: 78-01(E), Section: B.
500 $a Adviser: Pierre Germain.
502 $a Thesis (Ph.D.)--New York University, 2016.
520 $a This work is devoted to the study of some aspects of the well-posedness theory of evolution differential equations in mathematical physics.
520 $a In Part I we explore the effects of dispersion in incompressible, inviscid fluids in a variety of settings. In the absence of the strongly regularizing mechanism of viscosity, even in only two spatial dimensions effects such as the rotation of the earth or unidirectional gravitational forces are not understood well. For these we bring to light a mechanism that disperses waves, i.e. we show that in such systems waves or disturbances at different frequencies travel at distinct speeds, often also in different directions. On the one hand, this allows us to improve the well-posedness theory of a wide range of problems. In some scenarios this yields a theory that holds on a very large timespan. On the other hand, it may also resolve questions regarding the qualitative behavior of more complicated systems, where effects other than the dispersion play a dominant role.
520 $a In Part II we study the well-posedness theory of the so-called wave maps equation, which arises in quantum physics. The corresponding energy conservation law suggests a natural mathematical framework. For this problem, however, we show that in the physically relevant setting this consideration does not provide a satisfactory theory: For a given initial setup, the time evolution is not unique.
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