Quasiperiodic Solutions of the Generalized SQG Equation
Javier Gómez-Serrano · Alexandru D. Ionescu · Jaemin Park
Jun 2026 · Princeton University Press
Ebook
376
Pages
About this ebook
New, broadly applicable, parameter-free techniques for constructing stable quasiperiodic solutions of quasilinear evolution equations
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. The authors implement an ingenious scheme for building global quasiperiodic solutions without relying on external parameters, instead exploiting the natural structure of initial data to generate families of stable solutions. This approach offers a more robust framework for studying global solutions of quasilinear PDEs.
The book combines techniques from KAM theory, a Nash-Moser iteration scheme, and pseudodifferential calculus, and provides tools that extend beyond the specific SQG context and may prove useful for other evolution equations. Specifically, the authors establish the existence of quasiperiodic patch solutions for the generalized Surface Quasi-Geostrophic (SQG) equation across the parameter range $\alpha \in (1,2)$, in a neighborhood of the disk solution. These solutions exist globally in time without developing singularities, which sheds light on an important question about the behavior of geophysical fluid models. This work provides new insights into global dynamics in a mathematically challenging regime where standard perturbative methods are insufficient. And the techniques developed here offer potential applications to other evolution equations in mathematical physics, making this a valuable resource for researchers in partial differential equations, fluid dynamics, and related fields.
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. The authors implement an ingenious scheme for building global quasiperiodic solutions without relying on external parameters, instead exploiting the natural structure of initial data to generate families of stable solutions. This approach offers a more robust framework for studying global solutions of quasilinear PDEs.
The book combines techniques from KAM theory, a Nash-Moser iteration scheme, and pseudodifferential calculus, and provides tools that extend beyond the specific SQG context and may prove useful for other evolution equations. Specifically, the authors establish the existence of quasiperiodic patch solutions for the generalized Surface Quasi-Geostrophic (SQG) equation across the parameter range $\alpha \in (1,2)$, in a neighborhood of the disk solution. These solutions exist globally in time without developing singularities, which sheds light on an important question about the behavior of geophysical fluid models. This work provides new insights into global dynamics in a mathematically challenging regime where standard perturbative methods are insufficient. And the techniques developed here offer potential applications to other evolution equations in mathematical physics, making this a valuable resource for researchers in partial differential equations, fluid dynamics, and related fields.
New, broadly applicable, parameter-free techniques for constructing stable quasiperiodic solutions of quasilinear evolution equations
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations....
About the author
Javier Gómez-Serrano is professor of mathematics at Brown University. Alexandru D. Ionescu is professor of mathematics at Princeton University and the coauthor of The Einstein-Klein-Gordon Coupled System (Princeton). Jaemin Park is assistant professor of mathematics at Yonsei University in Seoul.
Javier Gómez-Serrano is professor of mathematics at Brown University. Alexandru D. Ionescu is professor of mathematics at Princeton University and the coauthor of The Einstein-Klein-Gordon Coupled System (Princeton). Jaemin Park is assistant professor of mathematics at Yonsei University in Seoul.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
