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On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation

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Date Issued:
2012
Summary:
In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek.
Title: On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation.
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Name(s): Kosloff, Leonardo.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: vi, 194 p. : ill.
Language(s): English
Summary: In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek.
Identifier: 811847377 (oclc), 3355570 (digitool), FADT3355570 (IID), fau:3941 (fedora)
Note(s): by Leonardo Kosloff.
Thesis (Ph.D.)--Florida Atlantic University, 2012.
Includes bibliography.
Mode of access: World Wide Web.
System requirements: Adobe Reader.
Subject(s): Fluid dynamics -- Data processing
Laplacian matrices
Attractors (Mathematics)
Differential equations, Partial
Held by: FBoU FAUER
Persistent Link to This Record: http://purl.flvc.org/FAU/3355570
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU