Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $

Zijun Chen; Shengkun Wu

doi:10.3934/cpaa.2021161

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2021, Volume 20, Issue 12: 4307-4319. Doi: 10.3934/cpaa.2021161

This issue Previous Article Partial regularity result for non-autonomous elliptic systems with general growth Next Article Time periodic solution to a two-species chemotaxis-Stokes system with

$ p $

-Laplacian diffusion

Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $

Zijun Chen^1, , and
Shengkun Wu^2,

1.
School of Mathematics, Monash University, VIC 3800, Australia
2.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

^* Corresponding author
^* Corresponding author

Received: April 2021

Revised: August 2021

Early access: September 2021

Published: December 2021

The second author is partially supported by the Chinese Scholarship Council (No. 201906050022)

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Abstract

The Zakharov system in dimension $ d = 2,3 $ is shown to have a local unique solution for any initial values in the space $ H^{s} \times H^{l} \times H^{l-1} $, where a new range of regularity $ (s, l) $ is given, especially at the line $ s-l = -1 $. The result is obtained mainly by the normal form reduction and the Strichartz estimates.

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Mathematics Subject Classification: Primary: 35Q55, 35L70.

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Figure 1. Region of regularity $ (s, l) $

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References

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