Well-Posedness and Long-Time Dynamics

Maleafisha Joseph Pekwa Stephen Tladi

ISBN 10: 6202515899 / ISBN 13: 9786202515894

Verlag: LAP LAMBERT Academic Publishing Mär 2020, 2020

Beschreibung

Neuware -This book focuses on the initial boundary value problem to the 3D quasigeostrophic and rotating Boussinesq equations. The equations are derived from conservation laws in continuum physics followed by the formulation of the problem as initial value problem on Hilbert spaces. By using Faedo-Galerkin approximation and semigroup technique, existence and uniqueness of solutions are proved. Additionally, the book outlines how Lyapunov functions can be used to assess energy stability criteria. The author also addresses singular problems for which the equation has parabolic structure (rotating Boussinesq equations for the atmosphere and ocean) and the singular limit is hyperbolic (quasigeostrophic equations for the atmosphere and ocean) in the asymptotic limit of small Rossby number. In particular, this approach gives as a corollary a constructive proof of the well-posedness of the problem of quasigeostrophic potential vorticity equations governing modons.Books on Demand GmbH, Überseering 33, 22297 Hamburg 64 pp. Englisch. Bestandsnummer des Verkäufers 9786202515894

Bibliografische Details

Titel: Well-Posedness and Long-Time Dynamics

Verlag: LAP LAMBERT Academic Publishing Mär 2020

Erscheinungsdatum: 2020

Einband: Taschenbuch

Zustand: Neu

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Inhaltsangabe:

This book focuses on the initial boundary value problem to the 3D quasigeostrophic and rotating Boussinesq equations. The equations are derived from conservation laws in continuum physics followed by the formulation of the problem as initial value problem on Hilbert spaces. By using Faedo-Galerkin approximation and semigroup technique, existence and uniqueness of solutions are proved. Additionally, the book outlines how Lyapunov functions can be used to assess energy stability criteria. The author also addresses singular problems for which the equation has parabolic structure (rotating Boussinesq equations for the atmosphere and ocean) and the singular limit is hyperbolic (quasigeostrophic equations for the atmosphere and ocean) in the asymptotic limit of small Rossby number. In particular, this approach gives as a corollary a constructive proof of the well-posedness of the problem of quasigeostrophic potential vorticity equations governing modons.