# On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation

@article{Muoz2021OnTL, title={On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation}, author={Claudio Mu{\~n}oz and Gustavo Ponce and Jean-Claude Saut}, journal={SIAM J. Math. Anal.}, year={2021}, volume={53}, pages={1029-1048} }

We show that the limit infimum, as time $\,t\,$ goes to infinity, of any uniformly bounded in time $H^{3/2+}\cap L^1$ solution to the Intermediate Long Wave equation converge to zero locally in an increasing-in-time region of space of order $\,t/\log(t)$. Also, for solutions with a mild $L^1$-norm growth in time is established that its limit infimum converge to zero, as time goes to infinity. This confirms the non existence of breathers and other solutions for the ILW model moving with a speed… Expand

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In this work, we study some special properties of smoothness concerning to the initial value problem associated with the Zakharov-Kuznetsov-(ZK) equation in the $n-$ dimensional setting, $n\geq 2.$ … Expand

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- 2020

Abstract We consider the Zakharov-Kutznesov (ZK) equation posed in with d = 2 and 3. Both equations are globally well-posed in In this article, we prove local energy decay of global solutions: if… Expand

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