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On The Study Of Global Solutions For A Nonlinear Equation

Haibo Yan, Ls Yong

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The well-posedness of global strong solutions for a nonlinear partial differential equation including the Novikov equation is established provided that its initial valuev0(x)satisfies a sign condition andv0(x)Hs(R)withs>3/2. If the initial valuev0(x)Hs(R)  (1s3/2)and the mean function of(1-x2)v0(x)satisfies the sign condition, it is proved that there exists at least one global weak solution to the equation in the spacev(t,x)L2([0,+),Hs(R))in the sense of distribution andvxL([0,+)×R).