On the Large-x Asymptotic of the Classical Solutions to the Non-Linear Benjamin Equation in Fractional Sobolev Spaces
Year: 2024
Type: article
Abstract: In this work, we study the large-x asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known Hs-well-posedness results to the case of the variable-weight Sobolev spaces. The spaces provide a direct control over the asymptotics of classical solutions and their weak derivatives, and permit us to compute the bulk large-x asymptotic of classical solutions explicitly in terms of input data. The asymptotic formula provides a precise description of the qualitative behaviour of classical solutions in weighted spaces and yields a number of weighted persistence and continuation results automatically.
Source: Fractal and Fractional
Authors: Nabendra Parumasur, Olabisi Aluko
Institution: University of KwaZulu-Natal
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,069
OpenAlex ID: W4403829560