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Lifespan of Solutions to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow

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Abstract

In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in [12], the lifespan of solution is shown to have a lower bound in the order of ε−2− if the strength of the perturbation is of the order of ε. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field on the electrically conducting fluid near the boundary.

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Authors and Affiliations

  1. School of Mathematical Sciences, and LSC-MOE, Shanghai Jiao Tong University, Shanghai, 200240, China

    Feng Xie

  2. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

    Tong Yang

  3. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Tong Yang

Authors
  1. Feng Xie
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  2. Tong Yang
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Correspondence to Feng Xie.

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This paper is dedicated to Professor Philippe G. Ciarlet on the occasion of his 80th birthday.

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Xie, F., Yang, T. Lifespan of Solutions to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow. Acta Math. Appl. Sin. Engl. Ser. 35, 209–229 (2019). https://doi.org/10.1007/s10255-019-0805-y

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  • DOI: https://doi.org/10.1007/s10255-019-0805-y

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