Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Robert Schippa"'
Publikováno v:
PUB-Publications at Bielefeld University
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00da7866466e95fcb12441788d9e2a2c
http://arxiv.org/abs/2212.14067
http://arxiv.org/abs/2212.14067
Autor:
Robert Schippa
Publikováno v:
Journal of Differential Equations. 299:111-153
A priori estimates and existence of real-valued periodic solutions to the modified Benjamin-Ono equation with initial data in H s for s > 1 / 4 are proved locally in time. The approach relies on frequency dependent time localization, after which disp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2de7b9d38ee9b0ca1d7d8013b33aa77a
https://doi.org/10.1016/j.jde.2021.07.019
https://doi.org/10.1016/j.jde.2021.07.019
Autor:
Robert Schippa
Publikováno v:
Discrete & Continuous Dynamical Systems - A. 40:5189-5215
A family of dispersive equations is considered which links a higher dimensional Benjamin-Ono equation and the Zakharov-Kuznetsov equation. For these fractional Zakharov-Kuznetsov equations new well-posedness results are proved using transversality an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f280266e3ef386fb731e0ab1e1d74639
https://doi.org/10.3934/dcds.2020225
https://doi.org/10.3934/dcds.2020225
Autor:
Rainer Mandel, Robert Schippa
Publikováno v:
Annales Henri Poincaré, 23, 1831–1882
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations of Fresne
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5907b78a9c4473242953c48491647cc9
https://publikationen.bibliothek.kit.edu/1000141756/139694532
https://publikationen.bibliothek.kit.edu/1000141756/139694532
Autor:
Robert Schippa
We prove new well-posedness results for energy-critical nonlinear Schrödinger equations in modulation spaces. This covers initial data with infinite mass and energy. The proof is carried out via bilinear refinements and adapted function spaces.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b9060966bc6ba611cc13d9beea41fdf
Autor:
Jan Rozendaal, Robert Schippa
New local smoothing estimates in Besov spaces adapted to the half-wave group are proved via $\ell^2$-decoupling. We apply these estimates to obtain new well-posedness results for the cubic nonlinear wave equation in two dimensions. The results are co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::feedef6a69fc8c659302cd75d9a56c33
Autor:
Robert Schippa
Publikováno v:
Journal of Fourier Analysis and Applications, 28 (2), Art.-Nr.: 16
We prove resolvent estimates in $L^p$-spaces for time-harmonic Maxwell's equations in two spatial dimensions and in three dimensions in the partially anisotropic case. In the two-dimensional case the estimates are sharp up to endpoints. We consider a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::199d031082de0c0df220a59ef458f88b
http://arxiv.org/abs/2103.16951
http://arxiv.org/abs/2103.16951
Autor:
Robert Schippa, Shinya Kinoshita
Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in the fully periodic case with initial data in Sobolev spaces $H^s$, $s>1$, is proved. Frequency dependent time localization is utilized to control the derivative nonlinearity.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::845997fe633fc1689b7b867820d02a8a
https://pub.uni-bielefeld.de/record/2951291
https://pub.uni-bielefeld.de/record/2951291
Autor:
Robert Schippa
Publikováno v:
Journal of Functional Analysis. 282:109352
We show new local $L^p$-smoothing estimates for the Schr\"odinger equation with initial data in modulation spaces via decoupling inequalities. Furthermore, we probe necessary conditions by Knapp-type examples for space-time estimates of solutions wit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27412c242aea8a3e822be7fa5ef2ac2a
https://doi.org/10.1016/j.jfa.2021.109352
https://doi.org/10.1016/j.jfa.2021.109352
Autor:
Robert Schippa
Publikováno v:
Trends in Mathematics ISBN: 9783030471736
Strichartz estimates are derived from l2-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature generalizing Galilean in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ac0e3f1282b645f1e9246292bc3de8a
https://doi.org/10.1007/978-3-030-47174-3_17
https://doi.org/10.1007/978-3-030-47174-3_17