Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids write by Hajime Koba. This book was released on 2014-10-03. Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids available in PDF, EPUB and Kindle. A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.
Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids
Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids write by Hajime Koba. This book was released on 2014-03-05. Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids available in PDF, EPUB and Kindle. A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.
Mathematical Analysis of the Navier-Stokes Equations
Mathematical Analysis of the Navier-Stokes Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Analysis of the Navier-Stokes Equations write by Matthias Hieber. This book was released on 2020-04-28. Mathematical Analysis of the Navier-Stokes Equations available in PDF, EPUB and Kindle. This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
Analysis of the Hodge Laplacian on the Heisenberg Group
Analysis of the Hodge Laplacian on the Heisenberg Group - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis of the Hodge Laplacian on the Heisenberg Group write by Detlef Muller. This book was released on 2014-12-20. Analysis of the Hodge Laplacian on the Heisenberg Group available in PDF, EPUB and Kindle. The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem write by A. L. Carey. This book was released on 2014-08-12. Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem available in PDF, EPUB and Kindle. A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.
