Dispersive equations and well-posedness of a linear equation of Airy type
Dispersive equations, characteristics curves, equation of the Airy type, KdV, Sobolev Spaces.
In this work we will study partial differential equations (PDE), especially those of the dispersive type. An important example of dispersive PDE is the Korteweg-de Vries. We prove the global well-posedness (GWP) of this equation in Sobolev spaces. We also prove GWP for a linear equation of the Airy type. The main tool will be Plancherel theorem and the method of characteristics.