Unique continuation for water waves and dispersive multiplier equations

Fuente: arXiv

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Detalles Bibliográficos
Autor principal:	Kirkeby, Adrian
Formato:	Preprint
Publicado:	2024
Materias:	Analysis of PDEs 35A02, 35B60, 35Q31, 35Q35
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

_version_	1866914426061324288
author	Kirkeby, Adrian
author_facet	Kirkeby, Adrian
contents	We show that if a solution to the water wave equation, for an arbitrary short time interval, is flat on an open set and the horizontal fluid velocity at the surface is zero on the same open set, then the wave must vanish everywhere for all times. In addition, we use a result from non-harmonic Fourier analysis to show that (1 + 1d) linear dispersive PDE with Fourier multipliers also have this unique continuation property, subject to a natural asymptotic growth condition on the multiplier symbol.
format	Preprint
id	arxiv_https___arxiv_org_abs_2401_14778
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Unique continuation for water waves and dispersive multiplier equations Kirkeby, Adrian Analysis of PDEs 35A02, 35B60, 35Q31, 35Q35 We show that if a solution to the water wave equation, for an arbitrary short time interval, is flat on an open set and the horizontal fluid velocity at the surface is zero on the same open set, then the wave must vanish everywhere for all times. In addition, we use a result from non-harmonic Fourier analysis to show that (1 + 1d) linear dispersive PDE with Fourier multipliers also have this unique continuation property, subject to a natural asymptotic growth condition on the multiplier symbol.
title	Unique continuation for water waves and dispersive multiplier equations
topic	Analysis of PDEs 35A02, 35B60, 35Q31, 35Q35
url	https://arxiv.org/abs/2401.14778

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