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pro vyhledávání: '"Herr Sebastian"'
This work is devoted to the stochastic Zakharov system in dimension four, which is the energy-critical dimension. First, we prove local well-posedness in the energy space $H^1\times L^2$ up to the maximal existence time and a blow-up alternative. Sec
Externí odkaz:
http://arxiv.org/abs/2410.05034
Autor:
Baňas, Ľubomír, Herr, Sebastian
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous problem. T
Externí odkaz:
http://arxiv.org/abs/2409.11366
We extend Bourgain's $L^2$-wellposedness result for the KP-II equation on $\mathbb{T}^2$ to initial data with negative Sobolev regularity. The key ingredient is a new linear $L^4$-Strichartz estimate which is effective on frequency-dependent time sca
Externí odkaz:
http://arxiv.org/abs/2407.12222
In this work we prove global well-posedness for the massive Maxwell-Dirac system in the Lorenz gauge in $\mathbb{R}^{1+3}$, for small, sufficiently smooth and decaying initial data, as well as modified scattering for the solutions. Heuristically we e
Externí odkaz:
http://arxiv.org/abs/2406.02460
Autor:
Herr, Sebastian, Kwak, Beomjong
Publikováno v:
Forum of Mathematics, Pi. 2024; 12:e14
The optimal $L^4$-Strichartz estimate for the Schr{\"o}dinger equation on the two-dimensional rational torus $\mathbb{T}^2$ is proved, which improves an estimate of Bourgain. A new method based on incidence geometry is used. The approach yields a str
Externí odkaz:
http://arxiv.org/abs/2309.14275
Autor:
Candy, Timothy, Herr, Sebastian
Massive and massless Dirac equations with Lorentz-covariant cubic nonlinearities are considered in spatial dimension $d=2,3$. Global well-posedness of the Cauchy problem for small initial data in scale-invariant Sobolev spaces and scattering of solut
Externí odkaz:
http://arxiv.org/abs/2308.12057
We study the three dimensional stochastic Zakharov system in the energy space, where the Schr\"odinger equation is driven by linear multiplicative noise and the wave equation is driven by additive noise. We prove the well-posedness of the system up t
Externí odkaz:
http://arxiv.org/abs/2301.02089
Publikováno v:
J. Funct. Anal. (2024), vol. 286, no. 4, article 110292
In this paper, low regularity local well-posedness results for the Kadomtsev--Petviashvili--I equation posed in spatial dimension $d =3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered.
Externí odkaz:
http://arxiv.org/abs/2212.14067
Autor:
Herr, Sebastian1 herr@math.uni-bielefeld.de, Beomjong Kwak2 beomjong@kaist.ac.kr
Publikováno v:
Forum of Mathematics, Pi. 9/9/2024, Vol. 12, p1-21. 21p.
Autor:
Richter, Aemilius Ludwig, author
Publikováno v:
Die evangelischen Kirchenordnungen des sechszehnten Jahrhunderts. Erster Band.: Urkunden und Regesten zur Geschichte des Rechts und der Verfassung der evangelischen Kirche in Deutschland.. :15-17