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Global stability of solutions with large initial conditions for the Navier–Stokes equations with damping

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Abstract

We prove that, under a suitable integrable condition, there is global stability of strong solutions for the 3D incompressible Navier–Stokes equations with a damping term which, consequently, provides a new class of global strong large solutions. Besides this, we prove that the system preserves helical symmetry and that, in this case, there is stability. Finally, if some parameters are small, we establish a connection between the stability of the system with and without the damping term.

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  1. Universidade Federal de Santa Catarina, Campus Blumenau, Blumenau-SC, Brazil

    Maicon J. Benvenutti

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  1. Maicon J. Benvenutti
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Communicated by Gustavo Ponce.

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Benvenutti, M.J. Global stability of solutions with large initial conditions for the Navier–Stokes equations with damping. São Paulo J. Math. Sci. 16, 915–931 (2022). https://doi.org/10.1007/s40863-022-00298-9

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