Article Dans Une Revue Journal of Functional Analysis Année : 2022

Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations

Résumé

We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $ i |\xi|^\alpha \xi $ , with $1 \le \alpha\le 2$, and that the nonlinear term is of the form $\partial_x f(u) $ where $f$ is the sum of an entire series with infinite radius of convergence. Under these conditions, we prove the unconditional local well-posedness of the Cauchy problem in $H(\T)$ for $s ≥ 1 − \frac{\alpha}{2(\alpha+1)}$ . This leads to some global existence results in the energy space $H^{\alpha/2}(\T)$, for $\alpha\in [\sqrt{2},2] $.

Dates et versions

hal-05577515 , version 1 (02-04-2026)

Identifiants

Citer

Luc Molinet, Tomoyuki Tanaka. Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations. Journal of Functional Analysis, 2022, 283 (1), pp.109490. ⟨10.1016/j.jfa.2022.109490⟩. ⟨hal-05577515⟩
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