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ON INTERNAL REGULARITY OF SOLUTIONS TO THE INITIAL VALUE PROBLEM FOR THE ZAKHAROV-KUZNETSOV EQUATION

Annotation

Internal regularity of weak solutions to the initial value problem for the Zakharov-Kuznetsov equation in the case of two spatial variables is considered. Results on existence of derivatives continuous in Hölder norms are established.

Keywords

Zakharov-Kuznetsov equation; initial value problem; internal regularity of solutions

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UDC

517.958

Pages

999-1006

References

1. Zakharov V.E., Kuznetsov E.A. O trekhmernykh solitonakh // Zhurn. eksper. teoret. fiz. 1974. T. 66. № 2. S. 594–597. 2. Faminskiy A.V. Zadacha Koshi dlya uravneniya Zakharova–Kuznetsova // Differentsial'nye uravneniya. 1995. T. 31. № 6. S. 1070–1081. 3. Levandosky J.L. Smoothing properties of nonlinear dispersive equations in two spatial dimensions // J. Differential Equ. 2001. V. 175. № 2. P. 275–352. 4. Faminskii A.V., Antonova A.P. On internal regularity of solutions to the initial value problem for the Zakharov–Kuznetsov equation // Progress in Partial Differential Equations, M. Reissig, M. Ruzhansky (eds.), Springer Proceedings in Mathematics & Statistics. 2013. V. 44. P. 53–74. 5. Kruzhkov S.N., Faminskiy A.V. Obobshchennye resheniya zadachi Koshi dlya uravneniya Kortevega de Friza // Matem. sbornik. 1983. T. 120. № 3. S. 396–425. 6. Faminskiy A.V. Zadacha Koshi dlya uravneniya Kortevega–de Friza i ego obobshcheniy // Trudy sem. im. I.G. Petrovskogo. 1988. T. 13. S. 56–105. 7. Kruzhkov S.N., Faminskiy A.V. O svoystvakh nepreryvnosti resheniy nekotorykh klassov nestatsionarnykh uravneniy // Vestnik Mosk. un-ta, ser. 1, Matematika, Mekhanika. 1983. T. 3. S. 29–34. 8. Antonova A.V., Faminskiy A.V. O regulyarnosti resheniy zadachi Koshi dlya uravneniya Zakharova–Kuznetsova v normakh Gel'dera // Matem. zametki. 2015. T. 97. Vyp. 1. S. 13–22.

Received

2015-06-11

Section of issue

Scientific articles

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