The Cauchy problem for critical and subcritical semilinear parabolic equations in Lr (II), initial data in critical Sobolev spaces Ḣ−s,rs

✍ Scribed by Wang Baoxiang

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 198 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00136-0

✦ Synopsis

By presenting some time-space L p -L r estimates, we will establish the local and global existence and uniqueness of solutions for semilinear parabolic equations with the Cauchy data in critical Sobolev spaces of negative indices. Our results contain the complex (derivative) Ginzburg-Landau equation and the Cahn-Hilliard equation as special cases.