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<p>We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Molinet, Global Existence and Finite-Time Blow-Up for a Nonlinear Nonlocal Evolution Equation, Commun. Math. Phys. 402 (2023), 3233–3252]. We investigate the spatial asymptotic behavior of its solutions. In particular, we observe the influence of the Coriolis effect, which, even for rapidly decaying initial data, yields local-in-time solutions that decay at the rate 1/|<i>x</i>|. Thereafter, we shed light on the optimality of this decay rate. On the other hand, the long-time behavior of solutions appears to be complex. In this context, we establish a blow-up criterion and investigate the persistence of the spatial decay rate for later times.</p>

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Remarks on the spatial asymptotic behavior of solutions to a 1D model of equatorial oceanic flows

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Manuel Fernando Cortez,
  • Oscar Jarrín

摘要

We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Molinet, Global Existence and Finite-Time Blow-Up for a Nonlinear Nonlocal Evolution Equation, Commun. Math. Phys. 402 (2023), 3233–3252]. We investigate the spatial asymptotic behavior of its solutions. In particular, we observe the influence of the Coriolis effect, which, even for rapidly decaying initial data, yields local-in-time solutions that decay at the rate 1/|x|. Thereafter, we shed light on the optimality of this decay rate. On the other hand, the long-time behavior of solutions appears to be complex. In this context, we establish a blow-up criterion and investigate the persistence of the spatial decay rate for later times.