Hitchhikerʼs guide to the fractional Sobolev spaces
E Di Nezza, G Palatucci, E Valdinoci - Bulletin des sciences …, 2012 - Elsevier
This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …
some of their possible definitions and their role in the trace theory. We prove continuous and …
[图书][B] The water waves problem: mathematical analysis and asymptotics
D Lannes - 2013 - books.google.com
Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …
Global solutions for the gravity water waves equation in dimension 3
P Germain, N Masmoudi, J Shatah - Annals of Mathematics, 2012 - JSTOR
We show existence of global solutions for the gravity water waves equation in dimension 3,
in the case of small data. The proof combines energy estimates, which yield control of L 2 …
in the case of small data. The proof combines energy estimates, which yield control of L 2 …
Exact steady periodic water waves with vorticity
A Constantin, W Strauss - Communications on Pure and …, 2004 - Wiley Online Library
We consider the classical water wave problem described by the Euler equations with a free
surface under the influence of gravity over a flat bottom. We construct two‐dimensional …
surface under the influence of gravity over a flat bottom. We construct two‐dimensional …
Time quasi-periodic gravity water waves in finite depth
We prove the existence and the linear stability of Cantor families of small amplitude time
quasi-periodic standing water wave solutions—namely periodic and even in the space …
quasi-periodic standing water wave solutions—namely periodic and even in the space …
[PDF][PDF] From the long jump random walk to the fractional Laplacian
E Valdinoci - arXiv preprint arXiv:0901.3261, 2009 - arxiv.org
arXiv:0901.3261v1 [math.PR] 21 Jan 2009 Page 1 arXiv:0901.3261v1 [math.PR] 21 Jan 2009
FROM THE LONG JUMP RANDOM WALK TO THE FRACTIONAL LAPLACIAN ENRICO …
FROM THE LONG JUMP RANDOM WALK TO THE FRACTIONAL LAPLACIAN ENRICO …
On the Cauchy problem for gravity water waves
We are interested in the system of gravity water waves equations without surface tension.
Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of …
Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of …
[图书][B] Quasi-periodic standing wave solutions of gravity-capillary water waves
M Berti, R Montalto - 2020 - ams.org
We prove the existence and the linear stability of small amplitude time quasi-periodic
standing wave solutions (ie periodic and even in the space variable $ x $) of a $2 …
standing wave solutions (ie periodic and even in the space variable $ x $) of a $2 …
Traveling water waves—the ebb and flow of two centuries
This survey covers the mathematical theory of steady water waves with an emphasis on
topics that are at the forefront of current research. These areas include: variational …
topics that are at the forefront of current research. These areas include: variational …
Traveling quasi-periodic water waves with constant vorticity
We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space
periodic water waves with vorticity. In particular, we prove the existence of small amplitude …
periodic water waves with vorticity. In particular, we prove the existence of small amplitude …