Isometric decomposition operators, function spaces E p,q and applications to nonlinear evolution equations

By using the isometric decomposition to the frequency spaces, we will introduce a new class of function spaces E p,q , which is a subspace of Gevrey 1-class G1(Rn) ⊂ C∞(Rn) for >0, and we will study the Cauchy problem for the nonlinear Schrödinger equation, the complex Ginzburg–Landau equation and the Navier–Stokes equation. Some well-posed results are obtained for the Cauchy data in E0 2,1, and the regularity behavior in Ect 2,1 ⊂ G1(Rn) for the complex Ginzburg–Landau equation and the Navier–Stokes equation is also obtained as time t 0. © 2005 Elsevier Inc. All rights reserved.