dedicated to professor kyu ya masuda on the occasion of his sixtieth birthdayWe consider the Navier Stokes system with slowly decaying external forcesWe show that the energy norm of a weak solution has non-uniform decay,under suitable conditions on the data f and a which make the energy of solution bounded in time. Also, we show the exact rate of the decay (uniform decay) of the energy,for external forces with a given explicit decay rate.
In this work, we consider alternative models for the propagation of bores. We consider the Boussinesq-Burgers system and the Kawahara-Burgers equation as models for the propagation of bores. We show the existence of travelling waves solutions corresponding to bore-like initial data.
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