Alexandru D. Ionescu,Fabio Pusateri
Global Regularity for 2D Water Waves with Surface Tension
Global Regularity for 2D Water Waves with Surface Tension
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Excellent- More about Global Regularity for 2D Water Waves with Surface Tension
The authors prove global regularity and modified scattering for the capillary waves system, developing a robust method to deal with strong singularities. They also introduce a new treatment of the Dirichlet-Neumann operator in dimension two, which is of independent interest.
\n Format: Paperback / softback
\n Length: 119 pages
\n Publication date: 30 October 2018
\n Publisher: American Mathematical Society
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The authors delve into the intricate realm of full irrotational water waves, encompassing surface tension and the absence of gravity in dimension two. They focus on the capillary waves system, a captivating model characterized by its slender structures. Through meticulous analysis, they establish global regularity and modified scattering for suitably small and localized perturbations of a flat interface.
A significant aspect of the authors' work lies in the development of a robust method known as the "quasilinear I-method." This method empowers them to tackle formidable singularities arising from time resonances in applications of the normal form method, famously known as the "division problem." As a result, they are able to explore a suitable class of perturbations with finite energy but without any additional momentum conditions.
Part of the authors' analysis relies on a novel approach to the Dirichlet-Neumann operator in dimension two, which holds independent interest. Consequently, the results presented in this paper stand on their own, offering a self-contained understanding of the subject matter.
The authors' exploration of full irrotational water waves extends beyond the capillary waves system, encompassing a broader range of physical phenomena. Their work contributes to our understanding of wave dynamics and sheds light on the intricate behavior of fluids in confined spaces. With their rigorous analysis and innovative methods, the authors have made significant strides in the field of mathematical physics, opening up new avenues for research and applications.
\n Weight: 204g\n
Dimension: 180 x 252 x 6 (mm)\n
ISBN-13: 9781470431037\n \n
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