Well-Posedness and Long-Time Dynamics - Tladi, Maleafisha Joseph Pekwa Stephen
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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…mehr

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Produktbeschreibung
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.
Autorenporträt
The author attended Clark University where he earned his Bachelor of Arts (BA), Summa Cum Laude, Phi Beta Kappa, with Highest Honors in Mathematics. He received his Master of Science (MSc), Magna Cum Laude, Sigma Xi from Brown University in Applied Mathematics and Engineering. He was conferred his PhD Degree from the University of Cape Town.