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
Author | : Cristian Gavrus,Sung-Jin Oh |
Publsiher | : American Mathematical Soc. |
Total Pages | : 94 |
Release | : 2020-05-13 |
Genre | : Education |
ISBN | : 9781470441111 |
Download Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data Book in PDF, Epub and Kindle
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.
Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data
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Author | : Cristian Dan Gavrus,Sung-Jin Oh |
Publsiher | : Unknown |
Total Pages | : 94 |
Release | : 2020 |
Genre | : Differential equations, Partial |
ISBN | : 147045808X |
Download Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data Book in PDF, Epub and Kindle
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.
Local Well Posedness and Break Down Criterion of the Incompressible Euler Equations with Free Boundary
Author | : Chao Wang |
Publsiher | : American Mathematical Soc. |
Total Pages | : 119 |
Release | : 2021-07-21 |
Genre | : Education |
ISBN | : 9781470446895 |
Download Local Well Posedness and Break Down Criterion of the Incompressible Euler Equations with Free Boundary Book in PDF, Epub and Kindle
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.
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
Author | : Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa |
Publsiher | : American Mathematical Soc. |
Total Pages | : 97 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442132 |
Download The Riesz Transform of Codimension Smaller Than One and the Wolff Energy Book in PDF, Epub and Kindle
Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
Global Smooth Solutions for the Inviscid SQG Equation
Author | : Angel Castro,Diego Cordoba,Javier Gomez-Serrano |
Publsiher | : American Mathematical Soc. |
Total Pages | : 89 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442149 |
Download Global Smooth Solutions for the Inviscid SQG Equation Book in PDF, Epub and Kindle
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
Author | : Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif |
Publsiher | : American Mathematical Soc. |
Total Pages | : 131 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442194 |
Download Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields Book in PDF, Epub and Kindle
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
Author | : Zhi Qi |
Publsiher | : American Mathematical Society |
Total Pages | : 123 |
Release | : 2021-02-10 |
Genre | : Mathematics |
ISBN | : 9781470443252 |
Download Theory of Fundamental Bessel Functions of High Rank Book in PDF, Epub and Kindle
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
Author | : Ulrich Bunke,David Gepner |
Publsiher | : American Mathematical Soc. |
Total Pages | : 177 |
Release | : 2021-06-21 |
Genre | : Education |
ISBN | : 9781470446857 |
Download Differential Function Spectra the Differential Becker Gottlieb Transfer and Applications to Differential Algebraic K Theory Book in PDF, Epub and Kindle
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.