On decay and regularly of solutions of the Benjamin-Ono equation

2025/09/08 by Felipe Linares, Gustavo Ponce, Linares, Felipe +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2509.06816

Abstract

We study persistence properties of solutions of the Benjamin-Ono equation in weighted Sobolev spaces. Roughly, we show that for β<7/2, the solution u(x,t) of the BO remains in the space L²(|x|^2β dx) if and only if its data u(x,0) belongs to this space and it is regular enough, i.e. u₀∈ H^β(\mathbb R).

Citations

• On decay and asymptotic properties of solutions to the Intermediate Long Wave equation
• Sharp well-posedness for the Benjamin--Ono equation
• Benjamin-Ono and Intermediate Long Wave equation : modeling, IST and PDE
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• The Kato-Ponce Inequality
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• On the decay properties of solutions to a class of Schrödinger equations
• On well-posedness for the Benjamin-Ono equation
• Global well-posedness of the Benjamin-Ono equation in low-regularity spaces
• Weighted norm inequalities for the conjugate function and Hilbert transform
• Nonlocal models for nonlinear, dispersive waves

Related

• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces
• The Cauchy Problem for Dissipative Benjamin-Ono equation in Weighted Sobolev spaces
• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces II
• On decay of the solutions for the dispersion generalized-Benjamin-Ono and Benjamin-Ono equations
• Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces