Department/College/UnitPhysical & Biological Sciences Division

TitleProfessor Emeritus of Mathematics

AffiliationFaculty

Web Siteschonbek.math.ucsc.edu

Primary Office LocationMcHenry Library
McHenry Building Room #4188

Mail StopMathematics Department

Biography, Education and Training

Licenciatura, University of Buenos Aires
Ph.D., University of Michigan

Research Interests

Maria Schonbek's research focuses on non-linear partial differential equations derived from models in fluid dynamics. The primary questions she is concerned with are related to the qualitative behavior of solutions, specifically questions concerning long-time behavior of solutions.

Understanding the behavior of solutions to equations for physical models is a first step in understanding the behavior of the world we live in.

In her research, Professor Schonbek has tried to make interdisciplinary connections since she believes that such work is fundamental to the progress of science.

Awards, Honors and Grants

American Mathematical Society Fellow

Selected Publications

• M. Schonbek: Estimates for the pressure and the Fourier transform of solutions and derivatives to the Navier-Stokes equations. Forthcoming.
• M. Cannone, F. Planchon, and M. Schonbek: Solutions to the incompressible Navier-Stokes equations in the half space. Submitted.
• Malek, Necas, Pocorny and Schonbek: On the possible singular solutions to the Navier-Stokes equations. Mathematische Nachrichten (1999), 97-114.
• M. Schonbek and G. K. Vallis: Energy decay of solutions of the Planetary geostrophic equations. Accepted for publication JMAA (1999).
• M. Schonbek, T. Schonbek, and E. Suli: Large-time behavior of solutions to the Magneto Hydrodynamics equations. Mathematische Annalen 304 (1996) 717-756
• Schonbek: Navier-Stokes space time decay revisited. Journal GAKUTO International Series Mathematical sciences and applications. Volume 35, 2011.
• Schonbeck, Carrillo, Canizo: Decay Rates for a class of Diffusive-dominated Interaction Equations. Journal of Mathematical analysis and appli- cations. Volume 389, Issue 1, Pages 541557. May 2012
• Schonbeck, Dai, Qing: Regularity of solutions to the liquid crystals systems in R2 and R3. Nonlinearity 25 513, 2012
• Schonbeck, Dai, Qing: Asymptotic Behavior of Solutions to Liquid Crystal Systems in R3. Communications in PDE, Volume 37, Issue 12, pages 2138-2164, January 2012
• Schonbeck, Carrillo, Gonzalez, Gualdani: Classical Solutions for a Fokker-Planck equation arising in Computational Neuroscience. (Accepted in CPDE)