Asymptotic stability of peakons for the Novikov equation

Orbital and asymptotic stability of a train of peakons for the Novikov equation

“…Proof. This is a consequence of Proposition 4.2 in [32] and the second inequality in (4.8). In fact, notice that the proof of that proposition only requires Lemmas 5.1 and 5.2 of the present work to hold.…”

“…Asymptotic stability results. About the asymptotic stability of peaked traveling waves, the case of a single peakon have recently been addressed and proved by the author by a proof based in a rigidity property of the Novikov equation (see [32] Theorems 1.2 and 1.3).…”

“…Before stating our main results we need to introduce the functional spaces where our initial data shall belong. Following the ideas of [9,15,16,27,32] we define…”

“…As we mentioned before, the main ingredient in the proof of Theorem 1.4 is a rigidity property of the Novikov equation ensuring that every H 1 -almost localized solution (c.f. Definition 1.1 in [32]) to equation (1.8) is actually a peakon. This latter property has been proved by introducing a new Lyapunov functional not related to the (not conserved) momentum of the equation.…”

“…Proof. The proof is somehow contained in the proof of Lemma 4.2, which at the same time is somehow contained in the proof of Lemma 3.2 in [32]. However, for the sake of completeness we show a sketch of the proof in the appendix.…”