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Author: Angel Castro
Publisher:
ISBN: 9781470462475
Category : Differential equations, Nonlinear
Languages : en
Pages :
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Book Description
"In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--
Author: Angel Castro
Publisher:
ISBN: 9781470462475
Category : Differential equations, Nonlinear
Languages : en
Pages :
Get Book
Book Description
"In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--
Author: Angel Castro
Publisher: American Mathematical Soc.
ISBN: 1470442140
Category : Mathematics
Languages : en
Pages : 89
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Book Description
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.
Author: Paul Godin
Publisher: American Mathematical Soc.
ISBN: 1470444216
Category : Education
Languages : en
Pages : 72
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Book Description
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.
Author: Chao Wang
Publisher: American Mathematical Soc.
ISBN: 1470446898
Category : Education
Languages : en
Pages : 119
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Book Description
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.
Author: Peter Constantin
Publisher: SIAM
ISBN: 1611974801
Category : Mathematics
Languages : en
Pages : 62
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Book Description
Analysis of Hydrodynamic Models presents a concise treatment of a number of partial differential equations of hydrodynamic origin, including the incompressible Euler equations, SQG, Boussinesq, incompressible porous medium, and Oldroyd-B. The author?s approach is based on properties of the particle trajectory maps and on analysis of the back-and-forth passage between the Lagrangian and the Eulerian descriptions. This concise, unified approach brings readers up to date on current open problems. This book is intended for graduate students and junior researchers in mathematics. This book is intended for graduate students and junior researchers in mathematics.
Author: Jonathan Gantner
Publisher: American Mathematical Society
ISBN: 1470442388
Category : Mathematics
Languages : en
Pages : 114
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Book Description
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.
Author: Paul M Feehan
Publisher: American Mathematical Society
ISBN: 1470443023
Category : Mathematics
Languages : en
Pages : 138
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Book Description
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.
Author: Zhi Qi
Publisher: American Mathematical Society
ISBN: 1470443252
Category : Mathematics
Languages : en
Pages : 123
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Book Description
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.
Author: Kazuyuki Hatada
Publisher: American Mathematical Soc.
ISBN: 1470443341
Category : Education
Languages : en
Pages : 165
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Book Description
View the abstract.
Author: Camille Male
Publisher: American Mathematical Society
ISBN: 1470442981
Category : Mathematics
Languages : en
Pages : 88
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Book Description
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.
