Well-posedness and analyticity of the Cauchy problem for the multi-component Novikov equation

Mi, Yongsheng; Guo, Boling; Luo, Ting

doi:10.1007/s00605-019-01297-3

Cited by 1 publication

(4 citation statements)

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“…For the second term in the integral in (27), by virtual of Lemma 2.4, we have 28) and ( 29) into( 27), it's easy to deduce that (30)…”

Section: Blow-up Criteriamentioning

confidence: 96%

“…where G = 1 2 e −|x| is Poisson kernel of Bessel potential operator (1 − ∂ 2 x ). For the second term in the integral in (27), by virtual of Lemma 2.4, we have…”

Section: Blow-up Criteriamentioning

confidence: 99%

“…Mi, Guo and Luo has just studied the local well-posedness of (1) in [27], in this section, we study the local well-posedness in critical Besov space. For the convenience of proof, we rewrite (1) into another equivalent form (4)…”

Section: Local Well-posednessmentioning

confidence: 99%

“…The well-posedness and global existence of Novikov equation has been studied by Wu, Yin [24,25], the Cauchy problem for GX equation was studied by Mi, Mu and Tao [26]. Very recently, the well-posedness for (1) has been proved by Mi, Guo and Luo [27]. To our best knowledge, the local well-posedness in critical Besov space, blow-up criteria and global existence have not be studied yet.…”

Section: Introductionmentioning

confidence: 99%

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Local well-posedness and global existence for a multi-component Novikov equation

2020

Applicable Analysis

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Considered herein is a multi-component Novikov equation, which admits bi-Hamiltonian structure, infinitely many conserved quantities and peaked solutions. In this paper, we deduce two blow-up criteria for this system and global existence for some two-component case in H s . Finally we verify that the system possesses peakons and periodic peakons.Correspondence should be addressed to Yuxi Hu; hu-yuxi@163.comNovikov equation was derived by Novikov, used the perturbative symmetry approach in classification of nonlocal PDES with three order nonlinearity. It should be note that Novikov equation is not symmetrical, which means (u, x) (−u, −x). Another interesting reduction for (2) is DP equation if we take v = 1,The DP equation was derived by Degasperis and Procesi [6] by applying the method of asymptotic integrability to a three order dispersive PDE. A big feature for DP equation is shock peakon [7,8] u(t, x) = − 1 t + k sgn(x)e −|x| .

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“…For the second term in the integral in (27), by virtual of Lemma 2.4, we have 28) and ( 29) into( 27), it's easy to deduce that (30)…”

Section: Blow-up Criteriamentioning

confidence: 96%

“…where G = 1 2 e −|x| is Poisson kernel of Bessel potential operator (1 − ∂ 2 x ). For the second term in the integral in (27), by virtual of Lemma 2.4, we have…”

Section: Blow-up Criteriamentioning

confidence: 99%

Section: Local Well-posednessmentioning

confidence: 99%