Nonlinear Stability Of Ekman Boundary Layers In Rotation Stratified Fluids
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Nonlinear Stability Of Ekman Boundary Layers In Rotation Stratified Fluids
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Author : Hajime Koba
language : en
Publisher:
Release Date : 2014-10-03
Nonlinear Stability Of Ekman Boundary Layers In Rotation Stratified Fluids written by Hajime Koba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-03 with Fluid mechanics categories.
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
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Author : Matthias Hieber
language : en
Publisher: Springer Nature
Release Date : 2020-04-28
Mathematical Analysis Of The Navier Stokes Equations written by Matthias Hieber and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
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
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Author : Detlef Muller
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Analysis Of The Hodge Laplacian On The Heisenberg Group written by Detlef Muller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
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
A Homology Theory For Smale Spaces written by Ian F. Putnam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.
The Optimal Version Of Hua S Fundamental Theorem Of Geometry Of Rectangular Matrices written by Peter Šemrl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\times n matrices over a division ring \mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples showing that it cannot be extended to the non-square case.
Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres written by J.-M. Delort and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Mathematics categories.
The Hamiltonian ∫X(∣∂tu∣2+∣∇u∣2+m2∣u∣2)dx, defined on functions on R×X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of u. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size ϵ give rise to almost global solutions, i.e. solutions defined on a time interval of length cNϵ−N for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.
The Theory Of Rotating Fluids written by Greenspan and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-07 with Mathematics categories.
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture written by Joel Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.
Index Theory For Locally Compact Noncommutative Geometries written by A. L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
A Geometric Theory For Hypergraph Matching written by Peter Keevash and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
The authors develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: `space barriers' from convex geometry, and `divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, they introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. They determine the essentially best possible minimum degree sequence for finding an almost perfect matching. Furthermore, their main result establishes the stability property: under the same degree assumption, if there is no perfect matching then there must be a space or divisibility barrier. This allows the use of the stability method in proving exact results. Besides recovering previous results, the authors apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in -graphs, and Fischer's conjecture on a multipartite form of the Hajnal-Szemerédi Theorem. Here they prove the exact result for tetrahedra and the asymptotic result for Fischer's conjecture; since the exact result for the latter is technical they defer it to a subsequent paper.
A Homology Theory For Smale Spaces
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Author : Ian F. Putnam
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29
The Optimal Version Of Hua S Fundamental Theorem Of Geometry Of Rectangular Matrices
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Author : Peter Šemrl
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29
Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres
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Author : J.-M. Delort
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06
The Theory Of Rotating Fluids
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Author : Greenspan
language : en
Publisher: CUP Archive
Release Date : 1968-07
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
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Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Index Theory For Locally Compact Noncommutative Geometries
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Author : A. L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12
A Geometric Theory For Hypergraph Matching
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Author : Peter Keevash
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20