Local existence and uniqueness in Besov spaces for the solution of a surface growth model with fractional power nonlinear term

Qingkai WANG; Gang WU

doi:10.7523/j.ucas.2023.052

Journal of University of Chinese Academy of Sciences >

2026 , Vol. 43 >Issue 3: 289 - 295

DOI: https://doi.org/10.7523/j.ucas.2023.052

Mathematics & Physics

Local existence and uniqueness in Besov spaces for the solution of a surface growth model with fractional power nonlinear term

Qingkai WANG ,
Gang WU

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School of Mathematical Sciences，University of Chinese Academy of Sciences，Beijing，100049，China

Received date: 2024-04-01

Accepted date: 2024-05-17

Online published: 2023-05-10

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Abstract

In this paper， we study the Cauchy problem for the 4-th order nonlinear equation $∂ t h + ∂ x 4 h + ∂ x 2 ∂ x h α = 0$ in one dimension for the initial data $h 0$ where $α ≥ 5$ and $α ∈ R$ . Making use of some subtle estimates of the corresponding linear equation and the nonlinear term， Littlewood-Paley theory， two-norm method， and contraction mapping principle， we obtain the local well-posedness result in nonhomogeneous Besov spaces.

Key words： surface growth model; Cauchy problem; well-posedness; Besov spaces; Littlewood-Paley theory

Cite this article

Qingkai WANG , Gang WU . Local existence and uniqueness in Besov spaces for the solution of a surface growth model with fractional power nonlinear term[J]. Journal of University of Chinese Academy of Sciences, 2026 , 43(3) : 289 -295 . DOI: 10.7523/j.ucas.2023.052

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