Wellposedness and scattering for the generalized Boussinesq equation

2021/08/30 by Jie Chen, Boling Guo, Chen, Jie +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2108.13117

openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show the local well-posedness of the generalized Boussinesq equation(gBQ) in L²(ℝ^d), H¹(ℝ^d) and obtain the global well-posedness, finite-time blowup and small initial data scattering of gBQ in energy space H¹(ℝ^d). Moreover, we obtain the large radial initial data scattering of defocusing case for d≥ 3 by using the method of Dodson-Murphy.

Citations

• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

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