Isometric decomposition operators, function spaces Ep,qλ and applications to nonlinear evolution equations
By Baoxiang Wang, Lifeng Zhao, Bo-ling Guo. 2006
225 citations recorded by the source corpus.
Abstract By using the isometric decomposition to the frequency spaces, we will introduce a new class of function spaces E p , q λ , which is a subspace of Gevrey 1-class G 1 ( R n ) ⊂ C ∞ ( R n ) for λ > 0 , and we will study the Cauchy problem for the nonlinear Schrodinger equation, the complex Ginzburg–Landau equation and the Navier–Stokes equation. Some well-posed results are obtained for the Cauchy data in E 2 , 1 0 , and the regularity behavior in E 2 , 1 ct ⊂ G 1 ( R n ) for the complex Ginzburg–Landau equation and the Navier–Stokes equation is also obtained as time t ↘ 0 .
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/af253274539550ad991a0ce28a33729cdf0d39fc
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Local well‐posedness of nonlinear dispersive equations on modulation spaces (2007, unknown): “A P] 6 A pr 2 00 0,s.”
- Sharpness of some properties of Wiener amalgam and modulation spaces (2008, unknown): “The sufficiency can be found in [10] (see also [23]).”
- Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations (2007, methodology): “However, Planchon [31], Molinet and Ribaud [25,26] mainly used the dyadic decomposition to the frequency space; the frequency-uniform decomposition was applied in [38,40], but the dispersive smooth effects were not involved in [38,40].”