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

By using the isometric decomposition to the frequency spaces, we will introduce a new class of function spaces , which is a subspace of Gevrey 1-class G1(Rn)⊂C∞(Rn) for λ>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 , and the regularity behavior in for the complex Ginzburg–Landau equation and the Navier–Stokes equation is also obtained as time t↘0.