Simão Correia, Filipe Oliveira, Jorge Drumond Silva
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引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5604-5633, August 2024. Abstract. We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e., the improved regularity of the integral term in Duhamel’s formula, with respect to the initial data and the corresponding regularity of the linear evolution, and how this property relates to local well-posedness. In a first step, we show how the problem generally reduces to the derivation of specific frequency-restricted estimates, which are multiplier estimates in the spatial frequency alone. Then, using a precise methodology, we prove these estimates for the specific cases of the modified Zakharov–Kuznetsov equation, the cubic and quintic nonlinear Schrödinger equation, and the quartic Korteweg–de Vries equation.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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