Overview
- A comprehensive review of water waves
- In depth discussion of Dirichlet to Neuman map
- Latest results on free boundary problems for compressible Euler
Part of the book series: Oberwolfach Seminars (OWS, volume 54)
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Keywords
- Water Waves
- Free Boundary Problems
- Compressible Euler
- Strichartz Estimates
- Paradifferential Calculus
About this book
This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler’s equations in general. A particular set of such problems is given by gaseous stars considered in a vacuum (modeled via the compressible Euler equations) as well as water waves in their full generality (seen as recasts of incompressible irrotational Euler equations). This is a broad research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
Authors and Affiliations
About the authors
Albert Ai is a postdoctoral researcher at the University of Wisconsin-Madison. He received his PhD from the University of California, Berkeley in 2019. His primary research interests include the analysis of nonlinear dispersive PDEs and harmonic analysis. In particular, he has worked on low regularity solutions of fluid models and wave equations.
Thomas Alazard is Director of Research at the CNRS and Associate Professor at the École normale supérieure Paris-Saclay. He received his PhD from the University of Bordeaux, France, in 2005. Previously, he worked at the Orsay mathematics department and at the École normale supérieure in Paris. His research focuses on the analysis of partial differential equations, a subject on which he has written several books.
Mihaela Ifrim is currently a Professor of Mathematics at the University of Wisconsin, Madison. She studied mathematics in Bucharest and at the University of California, Davis, where she received her Ph.D. in 2012. After a Simons postdoctoral fellowship at UC Berkeley, in 2017 she moved Madison, where she was a Sloan Research Fellow and a CAREER grant recipient. Her work spans many directions in nonlinear partial differential equations, including fluid dynamics and nonlinear dispersive flows, with an emphasis on free boundary problems and on the study of low regularity local and global dynamics of the solutions.
Daniel Tataru is a Distinguished Professor in Mathematics at the University of California, Berkeley. He is well known for his substantial contributions to dispersive pde's, also in connection to fluid dynamics, harmonic analysis, geometry, general relativity and free boundary problems. He studied mathematics at the University of Iasi, in Romania, and then at University of Virginia, where he received his Ph.D. in 1992. He spent almost a decade at Northwestern university, before moving to Berkeley. Among other honors, he is a Fellow of both the American Academy of Arts and Sciences and the European Academy of Sciences, as well as a Simons Investigator since 2013.
Bibliographic Information
Book Title: Free Boundary Problems in Fluid Dynamics
Authors: Albert Ai, Thomas Alazard, Mihaela Ifrim, Daniel Tataru
Series Title: Oberwolfach Seminars
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-60451-5Due: 20 July 2024
eBook ISBN: 978-3-031-60452-2Due: 20 July 2024
Series ISSN: 1661-237X
Series E-ISSN: 2296-5041
Edition Number: 1
Number of Pages: V, 248
Number of Illustrations: 2 b/w illustrations, 11 illustrations in colour