On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation
We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1) in any spatial dimension n⩾1 with rough initial data. For 1/2<α⩽1, we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/607028 |
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| author | Chunyan Huang |
| author_facet | Chunyan Huang |
| author_sort | Chunyan Huang |
| collection | DOAJ |
| description | We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1) in any spatial dimension n⩾1 with rough initial data. For 1/2<α⩽1, we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces Mp,11-2α(1⩽p⩽∞). For α=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in B˙∞,10(ℝn)∩M∞,10(ℝn). The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term. |
| format | Article |
| id | doaj-art-89c2f35441f64f498046946ace365fa9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-89c2f35441f64f498046946ace365fa92025-02-03T01:07:03ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/607028607028On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau EquationChunyan Huang0School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, ChinaWe study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1) in any spatial dimension n⩾1 with rough initial data. For 1/2<α⩽1, we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces Mp,11-2α(1⩽p⩽∞). For α=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in B˙∞,10(ℝn)∩M∞,10(ℝn). The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.http://dx.doi.org/10.1155/2014/607028 |
| spellingShingle | Chunyan Huang On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation Abstract and Applied Analysis |
| title | On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation |
| title_full | On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation |
| title_fullStr | On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation |
| title_full_unstemmed | On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation |
| title_short | On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation |
| title_sort | on the analyticity for the generalized quadratic derivative complex ginzburg landau equation |
| url | http://dx.doi.org/10.1155/2014/607028 |
| work_keys_str_mv | AT chunyanhuang ontheanalyticityforthegeneralizedquadraticderivativecomplexginzburglandauequation |