标题： 对广义的两组分Novikov系统的分析 显示英文标题

标题： Analysis on a generalized two-component Novikov system

摘要： 在本文中，我们研究具有弱耗散的广义两组分诺维科夫系统的柯西问题。我们首先通过使用卡托定理建立解的局部适定性。然后我们给出了有限时间内波浪破裂发生的必要充分条件。最后，我们研究了在一大类适度权重的加权$L^{p}(\mathbb{R})$空间中强解的持续性性质。 显示英文摘要

摘要： In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted $L^{p}(\mathbb{R})$ spaces for a large class of moderate weights.