Well-posedness of stochastic Korteweg-de Vries&amp;#8211;Benjamin&amp;#8211;Ono
equation

doi:10.1007/s11464-009-0057-x

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Front. Math. China ›› 2010, Vol. 5 ›› Issue (1) : 161-177. DOI: 10.1007/s11464-009-0057-x

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Well-posedness of stochastic Korteweg-de Vries–Benjamin–Ono equation

Guolian WANG¹,Boling GUO²,

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Abstract

In this paper, we consider the stochastic Korteweg-de Vries–Benjamin–Ono equation with white noise. Using Fourier restriction norm method and some basic inequalities, we obtain a local existence and uniqueness result for the solution of this problem. We also get global existence of the L²(R) solution.

Keywords

Korteweg-de Vries–Benjamin–Ono (KdV-BO) equation, Fourier restriction norm, [k / Z]-multiplier, cylindrical Wiener process

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Guolian WANG, Boling GUO,. Well-posedness of stochastic Korteweg-de Vries–Benjamin–Ono equation. Front. Math. China, 2010, 5(1): 161‒177 https://doi.org/10.1007/s11464-009-0057-x