Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations

By Baoxiang Wang, Chunyan Huang. 2007

180 citations recorded by the source corpus.

Abstract Sufficient and necessary conditions for the embeddings between Besov spaces B p , q s 1 and modulation spaces M p , q s 2 are obtained. Moreover, using the frequency-uniform decomposition method, we study the Cauchy problem for the generalized BO, KdV and NLS equations, for which the global well-posedness of solutions with the small rough data in certain modulation spaces M 2 , 1 s is shown.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/920332f0ae37c3470a495607bdc1e85deab2de72

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In Applied Mathematics

1. J. Toft
2. Nenad Teofanov
3. Fabio Di Nicola
4. Mitsuru Sugimoto
5. Stevan Pilipovic
6. Naohito Tomita
7. Michael Ruzhansky
8. Baoxiang Wang

In Mathematical Physics

1. Mitsuru Sugimoto
2. Fabio Di Nicola
3. Naohito Tomita
4. Michael Ruzhansky
5. Nenad Teofanov
6. Akihiko Miyachi
7. Stevan Pilipovic
8. J. Toft

In Statistical and Nonlinear Physics

1. Mitsuru Sugimoto
2. J. Toft
3. Naohito Tomita
4. Fabio Di Nicola
5. Jinsheng Han
6. Michael Ruzhansky
7. Stevan Pilipovic
8. Baoxiang Wang

Citations in the corpus

• Changes of variables in modulation and Wiener amalgam spaces (2008, methodology): “In particular, we establish a Beurling–Helson type result in this case as well by using the theory of Fourier integral operators in an essential way.”
• Sharpness of some properties of Wiener amalgam and modulation spaces (2008, unknown): “To recall the definition of these spaces, we first introduce the translation and modulation operators, defined by T x f ( t ) = f ( t − x ) and M ξ f ( t ) = e 2 π i ξ t f ( t ) , t , x , ξ ∈ d .”
• α-modulation spaces (I) scaling, embedding and algebraic properties (2014, background): “Their results were generalized to the cases 0 < p, q ≤ ∞ in [19, 20].”
• Micro-Local Analysis with Fourier Lebesgue Spaces. Part I (2011, background): “On the other hand, if s ∈ R and ρ ∈ [0] [1], then P ρ (R 2d ) contains ω(x, ξ) = ξ s , which seems to be the most important classes in the applications.”
• ESTIMATES FOR UNIMODULAR FOURIER MULTIPLIERS ON MODULATION SPACES (2009, result): “Notice that the above negative result shows that the Cauchy problem (1) is not locally wellposed in any M p,q, if p 6= 2 and α > 2. For positive results in this connection we refer to [1, 2, 5, 27 ]”