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<p>In this paper, we investigate the existence of mild solutions of the nonlinear fractional Rayleigh-Stokes problem for a generalized second grade fluid on an infinite interval. We firstly show the boundedness and continuity of solution operator. And then, by using a generalized Arzelà-Ascoli theorem and some new techniques, we get the compactness on the infinite interval. Moreover, we prove the existence of global mild solutions of nonlinear fractional Rayleigh-Stokes problem.</p>

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The nonlinear fractional Rayleigh-Stokes problem on an infinite interval

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • Jing Na Wang

摘要

In this paper, we investigate the existence of mild solutions of the nonlinear fractional Rayleigh-Stokes problem for a generalized second grade fluid on an infinite interval. We firstly show the boundedness and continuity of solution operator. And then, by using a generalized Arzelà-Ascoli theorem and some new techniques, we get the compactness on the infinite interval. Moreover, we prove the existence of global mild solutions of nonlinear fractional Rayleigh-Stokes problem.