关于色散Burgers型方程的Cauchy问题

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2023-01-01 DOI:10.1512/iumj.2023.72.9409

Ayman Rimah Said

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引用次数: 0

摘要

研究了paralinearised弱色散汉堡类型方程:∂涂+∂x [Tuu]−T∂徐2 D u +∂x | |α−1 u = 0,α∈]1、2(,其中包含的主要非线性“最差互动”条款,即低交互方面,常见的弱色散汉堡类型方程:∂涂+ u∂徐D +∂x | |α−1 u = 0,α∈]1、2 (,,)uoh∈H (D), D = T或r .通过paradifferential复杂Cole-Hopf类型测量[38]中介绍了变换,我们证明一个新的先验估计在H (D)的控制下∥

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On the Cauchy problem for dispersive Burgers type equations

We study the paralinearised weakly dispersive Burgers type equation: ∂tu+ ∂x[Tuu]− T ∂xu 2 u+ ∂x |D| α−1 u = 0, α ∈]1, 2[, which contains the main non linear ”worst interaction” terms, i.e low-high interaction terms, of the usual weakly dispersive Burgers type equation: ∂tu+ u∂xu+ ∂x |D| α−1 u = 0, α ∈]1, 2[, with u0 ∈ H (D), where D = T or R. Through a paradifferential complex Cole-Hopf type gauge transform we introduced in [38], we prove a new a priori estimate in H(D) under the control of ∥

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