Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals PDF Download
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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: 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: Stuart Margolis
Publisher: American Mathematical Society
ISBN: 1470450429
Category : Mathematics
Languages : en
Pages : 135
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Author: András Juhász
Publisher: American Mathematical Society
ISBN: 1470449722
Category : Mathematics
Languages : en
Pages : 174
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Author: Zhiwu Lin
Publisher: American Mathematical Society
ISBN: 1470450445
Category : Mathematics
Languages : en
Pages : 136
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Book Description
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Author: Haosui Duanmu
Publisher: American Mathematical Society
ISBN: 147045002X
Category : Mathematics
Languages : en
Pages : 114
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Author: Murat Akman
Publisher: American Mathematical Society
ISBN: 1470450526
Category : Mathematics
Languages : en
Pages : 115
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Author: Leonard Gross
Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111
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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: Abed Bounemoura
Publisher: American Mathematical Soc.
ISBN: 147044691X
Category : Education
Languages : en
Pages : 89
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Book Description
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity
Author: Yurii Kolomoitsev
Publisher: American Mathematical Society
ISBN: 1470447584
Category : Mathematics
Languages : en
Pages : 118
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