Global Cauchy problem for a Leray-α model

2017 ◽  
Vol 33 (1) ◽  
pp. 207-220
Author(s):  
Hua Qiu ◽  
Yi Du ◽  
Zheng-an Yao
Keyword(s):  
Cauchy Problem ◽  
Global Cauchy Problem

scholarly journals WAVE PROPAGATION AND SCATTERING FOR THE RS2 BRANE COSMOLOGY MODEL

2009 ◽  
Vol 06 (04) ◽  
pp. 809-861 ◽  
Author(s):  
ALAIN BACHELOT
Keyword(s):  
Cauchy Problem ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Asymptotic Completeness ◽  
Decay Estimates ◽  
Brane Cosmology ◽  
Dispersive Waves ◽  
Wave Operators ◽  
Global Cauchy Problem

We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

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