Generalized Huygens' principle for a reduced gravity two and a half layer model in dimension three

Zhigang Wu; Weike Wang

doi:10.3934/krm.2017046

Article Contents

2017, Volume 10, Issue 4: 1205-1233. Doi: 10.3934/krm.2017046

This issue Previous Article Diffusive limit with geometric correction of unsteady neutron transport equation Next Article The stability of contact discontinuity for compressible planar magnetohydrodynamics

Generalized Huygens' principle for a reduced gravity two and a half layer model in dimension three

Zhigang Wu^1, and
Weike Wang^2, ,

1.
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

* Corresponding author: Weike Wang
* Corresponding author: Weike Wang

Received: August 31, 2016

Revised: November 30, 2016

Published: November 2017

The research of Z.G. Wu was sponsored by Natural Science Foundation of Shanghai (No. 16ZR1402100) and the Fundamental Research Funds for the Central Universities (No. 2232015D3-33). The research of W.K. Wang was supported by Natural Science Foundation of China (No. 11231006)

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Abstract

The Cauchy problem of the reduced gravity two and a half layer model in dimension three isconsidered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit two kinds of the generalized Huygens' waves. It is a significant different phenomenon from the Navier-Stokes system. Lastly, as a byproduct, we also extend $L^2(\mathbb{R}^3)$-decay rate to $L^p(\mathbb{R}^3)$-decay rate with $p>1$.

Keywords:

Green's function,
reduced gravity two and a half layer model,
Huygens' principle.

Mathematics Subject Classification: Primary: 35J08, 35B40; Secondary: 35A09, 35Q35.

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