Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Erdoğan, Burak"'
Autor:
Erdogan, Burak, Green, William R.
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'ees Volume 151, July 2021, Pages 132-170
We investigate $L^1\to L^\infty$ dispersive estimates for the one dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural $t^{-\frac12}$ decay rate, which may be improved to $t^{-\frac32}$ at
Externí odkaz:
http://arxiv.org/abs/2011.13519
Publikováno v:
J. Differential Equations, 271, (2021), 152-185
We study the fourth order Schr\"odinger operator $H=(-\Delta)^2+V$ for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and study the dynamic effect of each on the $L^1\to L^\infty$ dispers
Externí odkaz:
http://arxiv.org/abs/1905.02890
We investigate $L^1\to L^\infty$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural $t^{-\frac12}$ decay rate, which may be improved to $t^{-\fr
Externí odkaz:
http://arxiv.org/abs/1807.00219
Autor:
Erdoğan, Burak, Shakan, George
We use exponential sums to study the fractal dimension of the graphs of solutions to linear dispersive PDE. Our techniques apply to Schr\"odinger, Airy, Boussinesq, the fractional Schr\"odinger, and the gravity and gravity-capillary water wave equati
Externí odkaz:
http://arxiv.org/abs/1803.00674
Publikováno v:
Comm. Math. Phys. 367 (2019), no. 1, 241-263
In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent,
Externí odkaz:
http://arxiv.org/abs/1706.05257
Publikováno v:
J. Funct. Anal 274 (2018), no. 7, 2139-2161
Let $H=-\Delta+V$ be a Schr\"odinger operator on $L^2(\mathbb R^2)$ with real-valued potential $V$, and let $H_0=-\Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{\pm}=s-\lim_{t\to \pm\infty} e^{itH}e^{-itH_0}$ are known to be b
Externí odkaz:
http://arxiv.org/abs/1706.01530
Autor:
Erdogan, Burak, Tzirakis, Nikolaos
In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of
Externí odkaz:
http://arxiv.org/abs/1609.07811
Publikováno v:
Amer. J. Math., 141, no. 5, Oct. 2019, 1217-1258
We investigate $L^1\to L^\infty$ dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two dimensional space o
Externí odkaz:
http://arxiv.org/abs/1609.05164
Autor:
Erdogan, Burak, Tzirakis, Nikolaos
In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the difference of the nonlinear and the linear evolution is
Externí odkaz:
http://arxiv.org/abs/1202.5268