论文标题
Fornberg-Whitham方程的经典解决方案
Classical Solutions of the Fornberg-Whitham Equation
论文作者
论文摘要
在本文中，我们证明了Fornberg-Whitham方程的$ C^1（\ Mathbb {r}）$（又称经典解决方案）中的适合性。为了实现这一目标，我们研究了其在拉格朗日框架下的薄弱表述。然后，将普通微分方程的基本定理应用于生成的半线性系统，然后我们构建了方程式的独特解决方案，该方程不断取决于初始数据。这些结果改善了Sobolev和Besov空间中的其他结果。
In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental theorem of ordinary differential equations to the generated semi-linear system, we then construct a unique solution to the equation that is continuously dependent on the initial data. These results improve upon others in Sobolev and Besov spaces.
