Regularity of solutions to nonlinear dispersive equations
The author studies the regularity of solutions of nonlinear dispersive equations under decay assumptions on the derivatives of the data. Thus he obtains conditions guaranteeing this solution to have the same regularity as that of the associated linear problem. Finally, the author remarks that by \textit{S. Klainerman} [Commun. Pure Appl. Math. 38, 321-332 (1985; Zbl 0635.35059)] a similar principle (the commutative properties of the D'Alembertian operator and the Lorentz group) was successfully used to show the existence of a global small solution to nonlinear wave equations.
scientific article; zbMATH DE number 4146510
scientific article