Periodic Cauchy problem for one two-dimensional generalization of the Benjamin–Ono equation in Sobolev spaces of low regularity

In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin–Ono equation ut+HΔu+uux=0,(x,y)∈T2,t∈R,u(x,y,0)=u0(x,y), where H denotes the Hilbert transform with respect to the variable x and Δ is the Laplacian with respect to the spatial variables x and y, is...

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Veröffentlicht in:	Nonlinear analysis 2019-11, Vol.188, p.50-69
Hauptverfasser:	Bustamante, Eddye, Jiménez Urrea, José, Mejía, Jorge
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Sprache:	eng
Schlagworte:	Benjamin–Ono equation Boundary value problems Cauchy problems Hilbert transformation Sobolev space Sobolev spaces Well posed problems Well-posedness
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creator	Bustamante, Eddye Jiménez Urrea, José Mejía, Jorge
description	In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin–Ono equation ut+HΔu+uux=0,(x,y)∈T2,t∈R,u(x,y,0)=u0(x,y), where H denotes the Hilbert transform with respect to the variable x and Δ is the Laplacian with respect to the spatial variables x and y, is locally well-posed in the periodic Sobolev space Hs(T2), with s>7∕4.
doi_str_mv	10.1016/j.na.2019.05.014
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subjects	Benjamin–Ono equation Boundary value problems Cauchy problems Hilbert transformation Sobolev space Sobolev spaces Well posed problems Well-posedness
title	Periodic Cauchy problem for one two-dimensional generalization of the Benjamin–Ono equation in Sobolev spaces of low regularity
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