2024
Hammadi Abidi, Guilong Gui, and Ping Zhang
On the global existence and uniqueness of solution to 2-D inhomogeneous incompressible Navier-Stokes equations in critical spaces
Journal of Differential Equations, 406: 126-173
2022
Guilong Gui and Ping Zhang
Semiclassical Limit of Gross-Pitaevskii Equation with Dirichlet Boundary Condition
SIAM Journal on Mathematical Analysis, 54(1): 1053-1104
2021
Hammadi Abidi and Guilong Gui
Global Well-Posedness for the 2-D Inhomogeneous Incompressible Navier-Stokes System with Large Initial Data in Critical Spaces
Archive for Rational Mechanics and Analysis, 242(3): 1533-1570
2021
Guilong Gui, Yue Liu, Wei Luo, and Zhaoyang Yin
On a two dimensional nonlocal shallow-water model
Advances in Mathematics, 392: Paper No. 108021, 1-44
2021
Guilong Gui
Lagrangian approach to global well-posedness of the viscous surface wave equations without surface tension
Peking Mathematical Journal, 4(1): 1-82
2019
Hammadi Abidi and Guilong Gui
Inviscid limit for axisymmetric Navier-Stokes-Boussinesq system
Communications in Mathematical Sciences, 17(6): 1625-1652
2019
Guilong Gui, Chao Wang, and Yuxi Wang
Local well-posedness of the vacuum free boundary of 3-D compressible Navier-Stokes equations
Calculus of Variations and Partial Differential Equations, 58(5): 35 pp
2019
Guilong Gui, Yue Liu, and Ting Luo
Model equations and traveling wave solutions for shallow-water waves with the Coriolis effect
Journal of Nonlinear Science, 29(3): 993-1039
2019
Guilong Gui, Yue Liu, and Junwei Sun
A nonlocal shallow-water model arising from the full water waves with the Coriolis effect
Journal of Mathematical Fluid Mechanics, 21(2): 29 pp
2018
Robin Ming Chen, Guilong Gui, and Yue Liu
On a shallow-water approximation to the Green-Naghdi equations with the Coriolis effect
Advances in Mathematics, 340: 106-137
2015
Guilong Gui and Yue Liu
Global well-posedness and blow-up of solutions for the Camassa-Holm equations with fractional dissipation
Mathematische Zeitschrift, 281(3-4): 993-1020
2014
Guilong Gui
Global well-posedness of the two-dimensional incompressible magnetohydrodynamics system with variable density and electrical conductivity
Journal of Functional Analysis, 267: 1488-1539
2013
Guilong Gui, Yue Liu, Peter J. Olver, and C. Qu
Wave-Breaking and Peakons for a Modified Camassa-Holm Equation
Communications in Mathematical Physics, 319(3): 731-759
2013
Hammadi Abidi, Guilong Gui, and Ping Zhang
Well-posedness of 3-D inhomogeneous Navier-Stokes equations with highly oscillatory initial velocity field
Journal de Mathématiques Pures et Appliquées, 100(9): 166-203
2013
Ying Fu, Guilong Gui, Yue Liu, and C. Qu
On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity
Journal of Differential Equations, 255(7): 1905-1938
2012
Guilong Gui, Yue Liu, and Min Zhu
On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation
International Mathematics Research Notices, 21: 4858-4903
2012
Hammadi Abidi, Guilong Gui, and Ping Zhang
On the Wellposedness of Three-Dimensional Inhomogeneous Navier-Stokes Equations in the Critical Spaces
Archive for Rational Mechanics and Analysis, 204(1): 189-230
2011
Guilong Gui, Jingchi Huang, and Ping Zhang
Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable
Journal of Functional Analysis, 261: 3181-3210
2011
Hammadi Abidi, Guilong Gui, and Ping Zhang
On the decay and stability to global solutions of the 3-D inhomogeneous Navier-Stokes equations
Communications on Pure & Applied Mathematics, 64: 832-881
2011
Guilong Gui and Yue Liu
On the Cauchy problem for the two-component Camassa-Holm system
Mathematische Zeitschrift, 268(1-2): 45-66
2011
Guilong Gui and Yue Liu
On the Cauchy problem for the Degasperis-Procesi equation
Quarterly of Applied Mathematics, 69(3): 445-464
2010
Guilong Gui and Yue Liu
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
Journal of Functional Analysis, 258(12): 4251-4278
2010
Guilong Gui and Ping Zhang
Stability to the global large solutions of 3-D Navier-Stokes Equations
Advances in Mathematics, 225(3): 1248-1284
2009
Guilong Gui and Ping Zhang
Global smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with variable viscosity
Chinese Annals of Mathematics, Series B, 30(5): 607-630
2008
Guilong Gui, Yue Liu, and Lixin Tian
Global existence and blow-up phenomena for the peakon b-family of equations
Indiana University Mathematics Journal, 57(3): 1209-1234
2007
Guilong Gui and Yue Liu
On the Cauchy problem for the Ostrovsky equation with positive dispersion
Communications in Partial Differential Equations, 32(10-12): 1895-1916
2005
Lixin Tian, Guilong Gui, and Yue Liu
On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
Communications in Mathematical Physics, 257(3): 667-701
