1.主要课题

1. 国家自然科学基金重点项目，非线性可积系统的几何结构和奇性分析（11631007），2017-2021，参与；

2. 国家自然科学基金面上项目，具有不光滑孤子解非线性色散波方程的奇性解和全局解（11471259）, 2015-2018, 主持，已结题；

3. 国家自然科学基金青年项目，具有尖峰孤子解浅水波系统的整体解和爆破解（11001219）, 2011-2013, 主持，已结题；

4. 陕西省杰出青年科学基金项目， 非线性可积系统的爆破解和整体解(2020JC-37) ，2020-2022，主持；

5. 陕西省自然科学基础研究计划面上项目， 具有不光滑孤子解的可积系统解的定性性质研究（2019JM-007），2019-2020， 主持；

6. 陕西省自然科学基础研究计划青年项目， 具有尖峰孤子解的推广Camassa-Holm方程解的定性性质（2014JQ1002），2014-2016，已结题；

7. 陕西省教育厅自然科学专项，一类浅水波系统解的性质研究（2010JK860），2010-2012，主持，已结题.

[1] Ying Fu*, Haiquan Wang, A note on the solution map for the periodic multi-dimensional Camassa-Holm-type system, Monatshefte für Mathematik,  (2021). https://doi.org/10.1007/s00605-021-01615-8.

[2] Haiquan Wang*,Gezi Chong, Lili Wu, A note on the solution map for the two-component Novikov system in Besov spaces, Journal of Evolution Equations , 2021, 21(2): 1809-1843 .

[3] Haiquan Wang*, Yu Guo, A note on the initial value problem for a higher-order Camassa–Holm equation, Mathematische Nachrichten , 2020, accepted .

[4] Yingying Li, Ying Fu, Changzheng Qu*, The two-component $\mu$- Camassa--Holm system with peaked solutions, Discrete and Continuous Dynamical Systems - Series A, 2020, 40(10): 5929-5954.

[5] Haiquan Wang*, Gezi Chong, On the initial value problem for the two-coupled Camassa–Holm system in Besov spaces, Monatshefte für Mathematik , 2020, 193(2): 479-505.

[6] Changzheng Qu, Ying Fu*, Curvature blow-up for the higher-order Camassa-Holm equations, Journal of Dynamics and Differential Equations, 2020, 32(4): 1901-1939.

[7] Changzheng Qu*, Ying Fu, On Cauchy problem and peakons of a two-component Novikov system, SCIENCE CHINA Mathematics, 2020,63(10): 1965-1996.

[8] Haiquan Wang, Ying Fu*, A note on the Cauchy problem for the periodic two-component Novikov system, Applicable Analysis, 2020, 99(6): 1042-1065.

[9] Ying Fu*, Juanjuan Gao, On the support of solutions to the fifth-order Kadomtsev–Petviashvili II equation in three-dimensional space, Applicable Analysis, 2018, 97(16): 2794-2817.

[10] Ying Fu, Changzheng Qu*, Well-posedness and wave breaking of the degenerate Novikov equation, J. Differential Equations，2017, 263(8): 4634-4657.

[11] Haiquan Wang, Ying Fu*, Non-uniform dependence on initial data for the two-component Novikov system, Journal of Mathematical Physics, 2017, 58: 021502,22pp.

[12] Haiquan Wang, Ying Fu*, Non-uniform dependence on initial data for the modified \mu-Camassa-Holm equation, Journal of Differential Equations, 2016, 261(11)：6099-6124.

[13] Ying Fu, A note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearity, Discrete Continuous Dynam. Systems, 2015, 35(5): 2011-2039.

[14] Changzheng Qu, Ying Fu, Yue Liu, Blow-up solutions and peakons to a generalized $\mu$-Camassa-Holm integrable equation, Comm. Math. Phys., 2014，331 (1):375-416.

[15] Changzheng Qu, Ying Fu, Yue Liu,  Well-posedness, wave breaking and peakons for a modified $\mu$-Camassa-Holm equation, Journal of Functional Analysis, 2014,266(2): 433-477.

[16] Ying Fu, Guilong Gui, Yue Liu, On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity, J. Differential Equations, 2013, 255：1905-1938.  

[17] Ying Fu, Yue Liu,  Changzheng Qu. On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations, Journal of Functional Analysis, 2012, 262: 3125-3158.

[18] Ying Fu, Changzheng Qu, Unique continuation and persistence properties of solutions of the 2-component Degasperis-procesi equations, Acta Math. Sci. Ser. B Engl. Ed., 2012, 32: 652-662.  

[19] Ying Fu, Yue Liu, Changzheng Qu , Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons, Math. Ann., 2010, 348(2): 415-448.

[20] Ying Fu, Changzheng Qu, Yichen Ma, Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations, Discrete Continuous Dynam. Systems, 2010, 27(3): 1025-1035.

[21] Changzheng  Qu，Ying Fu, On a new three-component Camassa-Holm equation with peakons, Commun. Theor. Phys., 2010, 53(2):223-230.

[22] Ying Fu, Changzheng Qu . Well posedness and blow-up solution for a new coupled Camassa-Holm equations with peakons, Journal of Mathematical Physics, 2009, 50: 012906, 25pp.  

[23] Ying Fu, Changzheng Qu. Unique continuation property for the Generalized Davey-Stewartson System in Rⁿ, 数学进展, 2013, 42(1): 95-105.

[24] Ying Fu, Changzheng Qu, Yichen Ma. On the unique continuation property for a coupled Schrödinger-KdV equation，数学进展,2010, 39(2): 169-178.

Latest update: September 29, 2021.

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