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1.

図書

図書
Raims Örlü ... [et al.], editors
出版情報: Cham : Springer, c2017  xv, 250 p. ; 25 cm
シリーズ名: Springer proceedings in physics ; v. 196
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2.

図書

図書
edited by Charles L. Fefferman, James C. Robinson, José L. Rodrigo
出版情報: Cambridge : Cambridge University Press, 2018  ix, 326 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 452
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3.

図書

図書
François Treves
出版情報: Cham : Springer, c2022  xiii, 1228 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; v. 359
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4.

図書

図書
Andrew Majda
出版情報: New York : Courant Institute of Mathematical Sciences, New York University , Providence, R.I : American Mathematical Society, 2003  ix, 234 p. ; 26 cm
シリーズ名: Courant lecture notes in mathematics ; 9
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目次情報: 続きを見る
Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
Two-Dimensional Exact Solutions / 1.2.:
Buoyancy and Stratification / 1.3.:
Jet Flows with Rotation and Stratification / 1.4.:
From Vertical Stratification to Shallow Water / 1.5.:
Some Remarkable Features of Stratified Flow / Chapter 2.:
Energy Principle / 2.1.:
Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.:
Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.:
Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.:
Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.:
More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.:
Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.:
Boussinesq Equations and Vorticity Stream Formulation / 3.1.:
Nonlinear Instability of Stratified Flows / 3.2.:
Shear Flows / 3.3.:
Some Background Facts on ODEs / 3.4.:
Rotating Shallow Water Theory / Chapter 4.:
Rotating Shallow Water Equations / 4.1.:
Conservation of Potential Vorticity / 4.2.:
Nonlinear Conservation of Energy / 4.3.:
Linear Theory for the Rotating Shallow Water Equations / 4.4.:
Nondimensional Form of the Rotating Shallow Water Equations / 4.5.:
Derivation of the Quasi-Geostrophic Equations / 4.6.:
The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.:
The Model Rotating Shallow Water Equations / 4.8.:
Preliminary Mathematical Considerations / 4.9.:
Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.:
Proof of the Convergence Theorem / 4.11.:
Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.:
Linear Wave Midlatitude Planetary Equations / 5.1.:
Dispersive Waves: General Properties / 5.2.:
Interpretation of Group Velocity / 5.3.:
Distant Propagation from a Localized Source / 5.4.:
WKB Methods for Linear Dispersive Waves / 5.5.:
Beyond Caustics: Eikonal Equation Revisited / 5.6.:
Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.:
Nonlinear WKB and the Boussinesq Equations / 5.8.:
Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.:
Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.:
The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.:
Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.:
The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.:
The Rotating Boussinesq Equations / 7.1.:
The Nondimensional Rotating Boussinesq Equations / 7.3.:
Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.:
Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.:
Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.:
Motivation for Fast-Wave Averaging / 8.1.:
A General Framework for Averaging over Fast Waves / 8.3.:
Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.:
The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.:
The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.:
Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.:
Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.:
The Equatorial Primitive Equations / 9.2.:
The Nonlinear Equatorial Long-Wave Equations / 9.3.:
A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.:
Bibliography
Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
5.

図書

図書
A. Bensoussan, J.-L. Lions
出版情報: Paris : Dunod, c1978  545 p. ; 25 cm
シリーズ名: Méthodes mathématiques de l'informatique ; 6
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6.

図書

図書
Carlos A. Berenstein, Milos A. Dostal
出版情報: Berlin ; New York : Springer-Verlag, 1972  v, 130 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 256
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7.

図書

図書
Philip Brenner, Vidar Thomée, Lars B. Wahlbin
出版情報: Berlin ; New York : Springer-Verlag, 1975  154 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 434
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8.

図書

図書
Alain Bensoussan, Jacques-Louis Lions ; English version edited, prepared, and produced by Trans-Inter-Scientia
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York : Sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1982  xi, 564 p. ; 23 cm
シリーズ名: Studies in mathematics and its applications ; v. 12
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9.

図書

図書
Manfred Kracht, Erwin Kreyszig
出版情報: New York : Wiley, c1988  xiv, 394 p. ; 24 cm
シリーズ名: Canadian Mathematical Society series of monographs and advanced texts
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10.

図書

図書
Ronald B. Guenther and John W. Lee
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1988  xii, 544 p. ; 25 cm
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