Non-uniform Dependence for the Novikov Equation in Besov Spaces

Springer Science and Business Media LLC - Tập 22 - Trang 1-10 - 2020
Jinlu Li1,2, Min Li3, Weipeng Zhu1
1School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
2School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, China
3School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, China

Tóm tắt

In this paper, we investigate the dependence on initial data of solutions to the Novikov equation. We show that the solution map is not uniformly continuous dependence on the initial data in Besov spaces $$B^s_{p,r}({\mathbb {R}}),\ s>\max \{1+\frac{1}{p},\frac{3}{2}\}$$ .

Tài liệu tham khảo

Bahouri, H., Chemin, J.Y., Danchin, R.: Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, vol. 343. Springer, Berlin (2011)

Constantin, A.: The Hamiltonian structure of the Camassa–Holm equation. Expos. Math. 15(1), 53–85 (1997)

Degasperis, A., Holm, D.D., Hone, A.N.W.: A new integral equation with peakon solutions. Theor. Math. Phys. 133, 1463–1474 (2002)

Degasperis, A., Procesi, M.: Asymptotic integrability. In: Gaeta, G. (ed.) Symmetry and Perturbation Theory (Rome 1998), pp. 23–37. World Science Publications, River Edge, NJ (1999)

Li, J., Yu, Y., Zhu, W.: Non-uniform dependence on initial data for the Euler equations in Besov spaces. arXiv:2001.03301

Toland, J.F.: Stokes waves. Topol. Methods Nonlinear Anal. 7(1), 1–48 (1996)