Global Smooth Solutions For The Inviscid Sqg Equation
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Global Smooth Solutions For The Inviscid Sqg Equation
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Author : Angel Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro 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 2020-09-28 with Mathematics categories.
In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
Global Smooth Solutions For The Inviscid Sqg Equation
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Author : Angel Castro
language : en
Publisher:
Release Date : 2020
Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Differential equations, Nonlinear categories.
"In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--
The 2d Compressible Euler Equations In Bounded Impermeable Domains With Corners
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Author : Paul Godin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
The 2d Compressible Euler Equations In Bounded Impermeable Domains With Corners written by Paul Godin 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 2021-06-21 with Education categories.
We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces.
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary
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Author : Chao Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary written by Chao Wang 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 2021-07-21 with Education categories.
In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms
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Author : Kazuyuki Hatada
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms written by Kazuyuki Hatada 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 2021-06-18 with Education categories.
View the abstract.
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals
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Author : Paul M Feehan
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals written by Paul M Feehan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Theory Of Fundamental Bessel Functions Of High Rank
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Author : Zhi Qi
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Theory Of Fundamental Bessel Functions Of High Rank written by Zhi Qi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
C Projective Geometry
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Author : David M Calderbank
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
C Projective Geometry written by David M Calderbank and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Traffic Distributions And Independence Permutation Invariant Random Matrices And The Three Notions Of Independence
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Author : Camille Male
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Traffic Distributions And Independence Permutation Invariant Random Matrices And The Three Notions Of Independence written by Camille Male and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators
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Author : Jonathan Gantner
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators written by Jonathan Gantner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.