Research Interests: 

My current research lies in the field of nonlinear partial differential equations, especially that related to some integrable systems (e.g., Camassa-Holm equation, Cubic (or modified) Camassa-Holm equation, Hunter-Saxton equation) and kinetic theory (e.g., Vlasov-Poisson system, Dyson's equation from Dyson Brownian motions, Keller-Segel equations). I mainly focus on the well-posedness theory of the equations.  

Preprints and Publications:

• Yu Gao, Cong Wang and Xiaoping Xue, Optimal decay rates and space-time analyticity of solutions to the Patlak-Keller-Segel equations,  Nonlinear Anal. RWA, 79, 2024.

• Yu Gao, Cong Wang and Xiaoping Xue, Global existence and spatial analyticity for a nonlocal flux with fractional diffusion,  J. Math. Phys., DOI: 10.1063/5.0151230, 2023.

• Cong Wang,  Yu Gao, and Xiaoping Xue, Quantitative estimates for space-time analyticity of solutions to the fractional Navier-Stokes equations,  Comm. Pure Appl. Anal.,  2023, 22(8), 2619-2645. 

• Yu Gao, Hao Liu, and Tak Kwong Wong,  Asymptotic behavior of conservative solutions to the Hunter-Saxton equation, SIAM J. Math. Anal., 2023, 55(5), 5483-5525.

• Yu Gao, On conservative sticky peakons to the modified Camassa-Holm equation,  J. Differential Equations,  2023, 365: 486-520.

• Yu Gao, Hao Liu, and Tak Kwong Wong, Stability of peakons of the Camassa-Holm equation beyond wave breaking, J. Math. Phys., 2022, 63(12): 121503.

•  Cong Wang,  Yu Gao, and Xiaoping Xue, Joint space-time analyticity of mild solutions to the Navier-Stokes equations,  J. Math. Anal. Appl, 2022, 515(2): 126428.

•  Yu Gao,  Hao Liu, and Tak Kwong Wong, Regularity structure of conservative solutions to the Hunter-Saxton equation,  SIAM J. Math. Anal., 2022, 54(1): 423-452. 

•  Fanqin Zeng, Yu Gao, and Xiaoping Xue, Global weak solutions to the generalized mCH equation via characteristics,  Discrete Contin. Dyn. Syst. Ser. B., 2022, 27(8): 4317-4329.

•   Yu Gao and Hao Liu, Global N-peakon weak solutions to a family of nonlinear equations, J. Differential Equations, 2021, 271: 343-355.

•  Yu Gao, Yuan Gao and Jian-Guo Liu, Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation, Quart. Appl. Math., 2020, 79: 55-102. 

•  Yu Gao, Lei Li and Jian-Guo Liu, Patched peakon weak solutions of the modified Camassa-Holm equation, Physica D, 2019, 390: 15-35. 

•  Yu Gao, Lei Li and Jian-Guo Liu, A dispersive regularization for the modified Camassa-Holm equation, SIAM J. Math. Anal., 2018, 50(3):2807-2838. 

•  Yu Gao and Jian-Guo Liu, The modified Camassa-Holm equation in Lagrangian coordinates, Discrete Contin. Dyn. Syst. Ser. B., 2018, 23(6):2545-2592. 

•  Yu Gao and Xiaoping Xue, Global existence and uniqueness of measure valued solutions to a Vlasov type equation with local alignment, Math. Methods Appl. Sci. 2017, 40:7640-7662.  

•  Yu Gao and Jian-Guo Liu, Global convergence of a sticky particle method for the modified Camassa-Holm equation, SIAM J. Math. Anal., 2017, 49(2):1267-1294.