Abstract
In this work, we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-Stewartson II system (hyperbolic-elliptic case). Arbitrary order mass convergence could be achieved by the suitable addition of correction terms, while keeping the first order accuracy in Hγ × Hγ+1 for initial data in Hγ+1 × Hγ+1 with γ > 1. The main theorem is that, up to some fixed time T, there exist constants τ0 and C depending only on T and \(||u|{|_{{L^\infty }\left( {(0,T);{H^{\gamma + 1}}} \right)}}\) such that, for any 0 < τ ≤ τ0, we have that
where un and vn denote the numerical solutions at tn = nτ. Moreover, the mass of the numerical solution M(un) satisfies that
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Ning’s work was supported by the NSFC (11901120), the Science and Technology Program of Guangzhou, China (2024A04J4027) and the Hao’s work was supported by the NSFC (12171356).
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Ning, C., Hao, C. & Wang, Y. A low-regularity Fourier integrator for the Davey-Stewartson II system with almost mass conservation. Acta Math Sci 44, 1536–1549 (2024). https://doi.org/10.1007/s10473-024-0419-1
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DOI: https://doi.org/10.1007/s10473-024-0419-1