Webrelaunch 2020

Dr. Robert Schippa

  • Project A5: Qualitative behavior of nonlinear Maxwell equations
  • Karlsruher Institut für Technologie
    Fakultät für Mathematik
    Institut für Analysis
    Englerstrasse 2
    76131 Karlsruhe
    Germany

Postdoctoral researcher within the CRC 1173, Project A5, since 1 April 2020

Current List of Courses
Semester Titel Typ
Summer Semester 2022 Proseminar
Winter Semester 2021/22 Seminar

Research interests

  • nonlinear dispersive equations
  • Harmonic Analysis on Euclidean space
  • quasilinear wave equations


Publications

  1. Generalized inhomogeneous Strichartz estimates. Discrete and Continuous Dynamical Systems - Series A (2017) Vol. 37, No. 6, pp. 3387-3410. Link
  2. Sharp Strichartz estimates in spherical coordinates. Communications on Pure and Applied Analysis (2017) Vol. 16, No. 6, pp. 2047-2051. Link
  3. On the existence of periodic solutions to the modified Korteweg–de Vries equation. Journal of Evolution Equations (2020) Vol. 20, pp.725-776 Link
  4. On Strichartz estimates from decoupling and applications. Mathematics of Wave Phenomena Link
  5. Local and global well-posedness for dispersion generalized Benjamin-Ono equations on the circle. Nonlinear Analysis:TMA. (2020). Vol. 196 Link
  6. On short-time bilinear Strichartz estimates and applications to the Shrira equation. Nonlinear Analysis: TMA. (2020) Vol. 198 Link
  7. On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations. Discrete and Continuous Dynamical Systems - Series A (2020) Vol. 40, No. 9, pp.5189-5215 Link
  8. (w/ Shinya Kinoshita) Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation. Journal of Functional Analysis (2021) Vol. 280, No. 6 Link
  9. (w/ Friedrich Klaus) A priori estimates for the derivative nonlinear Schrödinger equation. Link to Preprint (accepted to Funkcialaj Ekvacioj)
  10. (w/ Kihyun Kim) Low regularity well-posedness for generalized Benjamin-Ono equations on the circle. Link to Preprint (accepted to Journal of Hyperbolic Differential Equations)
  11. A priori estimates of periodic solutions to the modified Benjamin-Ono equation. Journal of Differential Equations (2021) Vol. 299, 111-153 Link
  12. (w/ Rainer Mandel) Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces. Link (Annales Henri Poincar'e: Journal of Mathematical and Theoretical Physics)
  13. On smoothing estimates in modulation spaces and the NLS with slowly decaying initial data. Journal of Functional Analysis (2022), Vol. 282 (5) Link
  14. Resolvent estimates for time-harmonic Maxwell's equations in the partially anisotropic case. Journal of Fourier Analysis and Applications (2022), Vol. 28 (2) Link
  15. (w/ Roland Schnaubelt) On quasilinear Maxwell equations in two dimensions.Link to Preprint (accepted to Pure and Applied Analysis)
  16. (w/ Jean-Claude Cuenin) Fourier transform of surface-carried measures of two-dimensional generic surfaces and applications.Link to Preprint (accepted to Communications on Pure and Applied Analysis)

Preprints

  1. (w/ Anna Muranova) Eigenvalues of the normalized complex Laplacian on finite electrical networks.Link to Preprint
  2. Well-posedness for Maxwell equations with Kerr nonlinearity in three dimensions via Strichartz estimates. Link to Preprint
  3. Oscillatory integral operators with homogeneous phase functions. Link to Preprint
  4. (w/ Dorothee Frey) Strichartz estimates for equations with structured Lipschitz coefficients. Link to Preprint
  5. (w/ Jan Rozendaal) Nonlinear wave equations with slowly decaying initial data. Link to Preprint
  6. Inifinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces Link to Preprint
  7. (w/ Akansha Sanwal) Low regularity well-posedness for KP-I equations: the dispersion generalised case Link to Preprint

Doctoral thesis

Short-time Fourier transform restriction phenomena and applications to nonlinear dispersive equations (Bielefeld University, 09/ 2019). Link