JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 56-63.doi: 10.6040/j.issn.1671-9352.0.2019.921

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Local Gevrey regularity and analyticity of the solutions to the initial value problem associated with the two-component Novikov system

WANG Hai-quan, CHONG Ge-zi   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Published:2020-06-01

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Abstract: Considered herein is the initial value problem for the two-component Novikov system. At first, the Gevrey regularity and analyticity of the solutions to this problem in Sobolev-Gevrey spaces G1r,s(R)×G1r,s-1(R)with s>3/2, r≥1 are investigated by making use of the generalized Ovsyannikov theorem. Next, the continuity of the solution map z0→z(t) is discussed. The results can be directly applied to Novikov equation.

Key words: two-component Novikov system, generalized Ovsyannikov theorem, regularity and analyticity, Sobolev-Gevrey spaces

CLC Number: 

  • O175.29
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