On the Navier–Stokes equations on surfaces
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Abstract We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $$\Sigma $$ Σ without boundary and flows along $$\Sigma $$ Σ . Local-in-time well-posedness is established in the framework of $$L_p$$ L p -$$L_q$$ L q -maximal regularity. We characterize the set of equilibria as the set of all Killing vector fields on $$\Sigma $$ Σ , and we show that each equilibrium on $$\Sigma $$ Σ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists globally and converges at an exponential rate to a (possibly different) equilibrium as time tends to infinity.
2018 ◽
Vol 16
(1)
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pp. 239-250
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Keyword(s):
2016 ◽
Vol 67
(2)
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Keyword(s):
2021 ◽
Vol 75
(2)
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pp. 223-348
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2016 ◽
Vol 472
(2187)
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pp. 20150728
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