Well-posedness for nonlinear dispersive equations
In this section we will study local and global well-posedness for a number of different equations where the techniques developed so far are relevant. The first example describes the interaction of three waves of different velocities. It is elementary and displays the role of adapted function spaces on an elementary level. The limitations of our current understanding become obvious as well: The result should remain true under small perturbations of the system, but I have no idea how to approach perturbed equations.
KeywordsFourier Multiplier Strichartz Estimate Unique Weak Solution Bilinear Estimate Nonlinear Dispersive Equation
Unable to display preview. Download preview PDF.