The Cauchy problem for critical and subcritical semilinear parabolic equations in \(L^r\). II: Initial data in critical Sobolev spaces \(\dot{H}^{-s,r^s}\)
The paper deals with the Cauchy problem in critical Sobolev spaces of negative indices for semilinear parabolic equations. Local and global existence and uniqueness is established by means of time-space \(L^p\)-\(L^r\) estimates. The complex (derivative) Ginzburg-Landau and the Cahn-Hilliard equations are special cases of these studied at the paper.
critical Sobolev spaces of negative indices
scientific article; zbMATH DE number 1879983