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Existence results for coupled nonlinear systems approximating the rotating MHD flow over a rotating sphere near the equator

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Abstract

We study a coupled nonlinear system of differential equation approximating the rotating MHD flow over a rotating sphere near the equator. In particular, using the Schauder fixed point theorem, we are able to establish existence of solutions. Other results on similar systems show that the question of existence in not obvious and, hence, that the present results are useful. Indeed, the work of McLeod in the 1970s shows some nonexistence results for similar problems. From here, we are also able to discuss some of the features of the obtained solutions. The observed behaviors of the solutions agree well with the numerical simulations present in the literature.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    Hamid Bellout

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Kuppalapalle Vajravelu & Robert A. Van Gorder

Authors
  1. Hamid Bellout
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  2. Kuppalapalle Vajravelu
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  3. Robert A. Van Gorder
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Correspondence to Hamid Bellout.

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Bellout, H., Vajravelu, K. & Van Gorder, R.A. Existence results for coupled nonlinear systems approximating the rotating MHD flow over a rotating sphere near the equator. Z. Angew. Math. Phys. 64, 83–100 (2013). https://doi.org/10.1007/s00033-012-0221-0

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  • DOI: https://doi.org/10.1007/s00033-012-0221-0

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