Some Recent Papers
- Long time behavior of solutions to the 3D compressible Euler equations with damping (with T. Sideris and B. Thomases).
Comm. Partial Differential Equations 28 (2003), no. 3-4, 795–816.
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- On two-dimensional sonic-subsonic flow
(with G.-Q. Chen, C. Dafermos, M. Slemrod).
Comm. Math. Phys. 271 (2007), no. 3, 635-647.
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- Vanishing viscosity method for transonic flow
(with G.-Q. Chen, M. Slemrod).
Arch. Rational Mech. Anal. 189 (2008), no. 1, 159-188.
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- Global solutions to the three-dimensional full compressible
magnetohydrodynamic flows (with X. Hu).
Commun. Math. Phys. 283 (2008), no. 1, 255-284.
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- Evolution of discontinuity and triple shock structure for a system of two-dimensional conservation laws (with G.-Q. Chen, X. Yang).
SIAM J. Math. Anal. 41 (2009), no. 1, 1-25.
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- Low Mach number limit of viscous compressible magnetohydrodynamic flows (with X. Hu).
SIAM J. Math. Anal. 41 (2009), no. 3, 1272-1294.
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- Conservation laws: transonic flow and differential geometry (with G.-Q. Chen, M. Slemrod).
Hyperbolic problems: theory, numerics and applications, 217-226,
Proc. Sympos. Appl. Math., 67, Part 1, Amer. Math. Soc., Providence, RI, 2009.
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- Isometric immersions and compensated compactness (with G.-Q. Chen, and M. Slemrod).
Commun. Math. Phys. 294 (2010), no. 2, 411-437.
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- A fluid dynamic formulation of the isometric embedding problem in
differential geometry (with G.-Q. Chen, M. Slemrod).
Quart. Appl. Math. 68 (2010), no. 1, 73-80.
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- Formation of singularities of solutions to the three-dimensional Euler-Boltzmann
equations in radiation hydrodynamics (with P. Jiang). Nonlinearity 23 (2010), no. 4, 809-821.
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- Weak continuity of the Gauss-Codazzi-Ricci system for isometric embedding
(with G.-Q. Chen, and M. Slemrod).
Proc. Amer. Math. Soc. 138 (2010), no. 5, 1843-1852.
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- Global solution to the three-dimensional incompressible flow of liquid crystals (with X. Hu).
Comm. Math. Phys. 296 (2010), no. 3, 861-880.
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- Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows
(with X. Hu).
Arch. Ration. Mech. Anal. 197 (2010), no. 1, 203-238.
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- Global existence for the multi-dimensional compressible viscoelastic flows (with X. Hu).
J. Differential Equations 250 (2011), no. 2, 1200-1231.
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- Formation of singularity for compressible viscoelasticity (with X. Hu),
Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), no. 1, 109-128.
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- Global weak solution and large-time behavior for the compressible flow of liquid crystals (with C. Yu).
Arch. Ration. Mech. Anal. 204 (2012), no. 3, 881-915.
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- On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a
bounded domain (with F. Jiang, S. Jiang), J. Functional Anal. 265 (2013), no. 12, 3369-3397.
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- Entropy, elasticity, and the isometric embedding problem (with G.-Q. Chen and M. Slemrod).
Hyperbolic Conservation Laws and Related Analysis with Applications, 95-112, Springer,
2014. PDF
- Global weak solutions to the equations of compressible flow of nematic liquid crystals in two dimensions (with F. Jiang, S. Jiang),
Arch. Ration. Mech. Anal. 214 (2014), no. 2, 403-451.
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- Incompressible limit for the compressible flow of liquid crystals (with C. Yu).
J. Mathematical Fluid Mechanics 16 (2014), no. 4, 771-786.
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- Global weak solution for a coupled compressible Navier-Stokes and Q-tensor system (with X. Xu, C. Yu).
Commun. Math. Sci. 13 (2015), no. 1, 49-82.
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- Global weak solution to the inhomogeneous Navier-Stokes-Vlasov equations (with C. Yu).
J. Differential Equations 259 (2015), no. 8, 3976-4008.
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- Isometric immersions of surfaces with two classes of metrics and negative Gauss curvature
(with W. Cao and F. Huang). Arch. Ration. Mech. Anal. 218 (2015), no. 3, 1431-1457.
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- Rectilinear vortex sheets of inviscid liquid-gas two-phase flow: linear stability (with L. Ruan, S. Weng, C. Zhu).
Commun. Math. Sci. 14 (2016), no. 3, 735-776.
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- A priori estimates for the free boundary problem of incompressible neo-Hookean elastodynamics (with C. Hao).
J. Differential Equations 261 (2016), no. 1, 712-737.
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- Global weak solution to the magnetohydrodynamic and Vlasov equations (with M. Chen and J. Hu).
J. Math. Fluid Mech. 18 (2016), no. 2, 343-360.
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- Isometric immersion of surface with negative Gauss curvature and the Lax-Friedrichs scheme
(with W. Cao and F. Huang).
SIAM J. Math. Anal. 48 (2016), no. 3, 2227-2249.
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- Linear stability of compressible vortex sheets in two-dimensional elastodynamics (with M. Chen, J. Hu).
Adv. Math. 311 (2017), 18-60.
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- Strong solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck equations: Global existence
near the equilibrium and large time behavior (with F. Li and Y. Mu).
SIAM J. Math. Anal. 49 (2017), no. 2, 984-1026.
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- Global existence and regularity of solutions for active liquid crystals
(with G.-Q. Chen, A. Majumdar and R. Zhang). J. Differential Equations 263 (2017), no. 1, 202-239.
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- Fluids, elasticity, geometry, and the existence of wrinkled solutions
(with A. Acharya, G.-Q. Chen, S. Li, M. Slemrod). Arch. Rational Mech. Anal. 226 (2017), no. 3, 1009-1060.
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- Isometric embedding via strongly symmetric positive systems
(with Gui-Qiang Chen, Jeanne Clelland, Marshall Slemrod, and Deane Yang).
Asian J. Math. 22 (2018), no. 1, 1-40.
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- Fluids, geometry, and the onset of Navier-Stokes turbulence in three space dimensions
(with G.-Q. Chen, M. Slemrod).
Physica D 376-377 (2018), 23-30.
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- Global weak solutions for the compressible active liquid crystal system
(with G.-Q. Chen, A. Majumdar and R. Zhang).
SIAM J. Math. Anal. 50 (2018), no. 4, 3632-3675.
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- Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite
nozzle
(with F. Huang, J. Kuang, W. Xiang). J. Differential Equations 266 (2019), 4337–4376.
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- Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions
(with L. Rebholz, Z. Wang, K. Zhao and C. Zerfas). Discrete Contin. Dyn. Syst. 39 (2019), no. 7, 3789-3838.
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- Well-posedness of nonisentropic Euler equations with physical vacuum
(with Y. Geng, Y. Li, and R. Xu). Interfaces Free Bound. 21 (2019), no. 2, 231-266.
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- Linear stability of compressible vortex sheets in 2D elastodynamics: variable coefficients
(with M. Chen, J. Hu). Math. Ann. 376 (2020), 863-912.
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- Energy equality in compressible fluids with physical boundaries
(with M. Chen, Z. Liang, R. Xu). SIAM J. Math. Anal. 52 (2020), no. 2, 1363-1385.
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- Global regularity of the three-dimensional fractional micropolar equations (with J. Wu, Z. Ye).
J. Math. Fluid Mech. 22 (2020), no. 2, 28.
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- Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional
compressible Navier-Stokes equations
(with L. Li and Y. Wang). Commun. Math. Phys. 376 (2020), 353-384.
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- Nonlinear stability and existence of compressible vortex sheets in 2D elastodynamics
(with M. Chen, J. Hu, T. Wang, D. Yuan}. J. Differential Equations. 269 (2020), no. 9, 6899–6940.
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- Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
(with C.-J. Liu, F. Xie, T. Yang). J. Funct. Anal. 279 (2020), no. 7, 108637.
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- Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows
(with Y. Mu). Calc. Var. Partial Differential Equations 59 (2020), no. 4, 110.
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- Stationary Cahn–Hilliard–Navier–Stokes equations for the diffuse interface model of compressible flows (with Z. Liang).
Math. Models Methods Appl. Sci. 30 (2020), no. 12, 2445-2486.
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- Cauchy problem of a system of parabolic conservation laws arising from the singular Keller-Segel model
in multi-dimensions (with Z. Wang and K. Zhao).
Indiana Univ. Math. J. 70 (2021), no. 1, 1-47.
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- Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions
(with T. Li, F. Wang, Z. Wang, K. Zhao).
Commun. Math. Sci. 19 (2021), no. 1, 229-272.
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- A rigidity property for the Novikov equation and the asymptotic stability of peakons (with M. Chen, W. Lian, R. Xu).
Arch. Ration. Mech. Anal. 241 (2021), no. 1, 497-533.
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- Stability of transonic contact discontinuity for two-dimensional steady compressible Euler flows in a finitely long nozzle (with F. Huang, J. Kuang, W. Xiang). Ann. PDE 7 (2021), no. 2, Paper No. 23, 96 pp.
https://doi.org/10.1007/s40818-021-00113-2.
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- Vanishing dissipation limit to the planar rarefaction wave
for the three-dimensional compressible Navier-Stokes-Fourier equations (with L. Li, Y. Wang).
J. Funct. Anal. 283 (2022), no. 2, 109499.
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- A Kato-type criterion for vanishing viscosity near the Onsager's critical regularity (with M. Chen and Z. Liang).
Arch. Ration. Mech. Anal. 246 (2022), no. 2-3, 535–559.
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- Inviscid limit of compressible viscoelastic equations with the no-slip boundary condition (with F. Xie).
J. Differential Equations 353 (2023), 63-113.
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- Stabilization effect of elasticity on three-dimensional compressible vortex sheets (with R. M. Chen, F. Huang, D. Yuan). J. Math. Pures Appl. 172 (2023), 105-138. PDF
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