In this paper, we consider the Zakharov-Kuznetsov equation in 3D, with a dissipative term of order $ 0 < \alpha \leq 2 $ in the $ x $ direction. We prove that the problem is locally well-posed in $ H^{s}( { I\!\!R}^3) $, for $ s > 1-\frac{\alpha}{2} $, and by an a priori energy estimate, we prove that the problem is globally well-posed in $ H^{1}( { I\!\!R}^3) $.

中文翻译：

---

3D耗散Zakharov-Kuznetsov方程在能量空间中的局部和全局适定性

在本文中，我们考虑3D的Zakharov-Kuznetsov方程，其耗散项在$ x $方向上为$ 0 <\ alpha \ leq 2 $。我们证明问题在$ H ^ {s}（{I \！\！R} ^ 3）$中局部存在，当$ s> 1- \ frac {\ alpha} {2} $时，作为先验能量估计，我们证明问题在$ H ^ {1}（{I \！\！R} ^ 3）$中是恰当的。