Some L¹-L¹ estimates for solutions to visco-elastic damped σ-evolution models

2019/11/15 by Tuan Anh Dao, Dao, Tuan Anh
Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1911.06563

Abstract

This note is to conclude L¹-L¹ estimates for solutions to the following Cauchy problem for visco-elastic damped σ-evolution models: \begincases u_tt+ (-Δ)^σu+ (-Δ)^σu_t = 0, amp; x∈ ℝⁿ, t ≥ 0,
u(0,x)= u₀(x), u_t(0,x)=u₁(x), amp; x∈ ℝⁿ, \endcases where σ> 1, in all space dimensions n≥ 1.

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