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On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation

Zhaoyang Yin

Open publisher page 39 citations

Abstract

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data. 1

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What this paper is about

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data. 1

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OpenAlex reports 39 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data. 1

Key concepts: Mathematics, Dispersive partial differential equation, Wave equation, Initial value problem, Mathematical analysis, Cauchy problem, Cauchy distribution, Partial differential equation

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