Global Well Posedness Of High Dimensional Maxwell Dirac For Small Critical Data
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Global Well Posedness Of High Dimensional Maxwell Dirac For Small Critical Data
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Author : Cristian Gavrus
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
Global Well Posedness Of High Dimensional Maxwell Dirac For Small Critical Data written by Cristian Gavrus 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 2020-05-13 with Education categories.
In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.
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.
Global Well Posedness Of High Dimensional Maxwell Dirac For Small Critical Data
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Author : Cristian Dan Gavrus
language : en
Publisher:
Release Date : 2020
Global Well Posedness Of High Dimensional Maxwell Dirac For Small Critical Data written by Cristian Dan Gavrus 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, Partial categories.
In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on \mathbb{R}^{1+d} (d\geq 4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell-Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell-Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Kri.
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.
Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields
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Author : Lisa Berger
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger 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.
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.
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.
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory written by Ulrich Bunke 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 develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Paley Wiener Theorems For A P Adic Spherical Variety
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Author : Patrick Delorme
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Paley Wiener Theorems For A P Adic Spherical Variety written by Patrick Delorme 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.
Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps
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Author : Pierre Albin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps written by Pierre Albin 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.
Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties
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Author : Hiroshi Iritani
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties written by Hiroshi Iritani 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.
Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.