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.   PDF On two-dimensional sonic-subsonic flow (with G.-Q. Chen, C. Dafermos, M. Slemrod). Comm. Math. Phys. 271 (2007), no. 3, 635-647.   PDF Vanishing viscosity method for transonic flow (with G.-Q. Chen, M. Slemrod). Arch. Rational Mech. Anal. 189 (2008), no. 1, 159-188.   PDF Global solutions to the three-dimensional full compressible magnetohydrodynamic flows (with X. Hu). Commun. Math. Phys. 283 (2008), no. 1, 255-284.   PDF 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.   PDF Low Mach number limit of viscous compressible magnetohydrodynamic flows (with X. Hu). SIAM J. Math. Anal. 41 (2009), no. 3, 1272-1294.   PDF 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.   PDF Isometric immersions and compensated compactness (with G.-Q. Chen, and M. Slemrod). Commun. Math. Phys. 294 (2010), no. 2, 411-437.   PDF 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.   PDF 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.   PDF 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.   PDF Global solution to the three-dimensional incompressible flow of liquid crystals (with X. Hu). Comm. Math. Phys. 296 (2010), no. 3, 861-880.   PDF 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.   PDF Global existence for the multi-dimensional compressible viscoelastic flows (with X. Hu). J. Differential Equations 250 (2011), no. 2, 1200-1231.   PDF Formation of singularity for compressible viscoelasticity (with X. Hu), Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), no. 1, 109-128.   PDF 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.   PDF 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.   PDF 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.   PDF Incompressible limit for the compressible flow of liquid crystals (with C. Yu). J. Mathematical Fluid Mechanics 16 (2014), no. 4, 771-786.   PDF 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.   PDF Global weak solution to the inhomogeneous Navier-Stokes-Vlasov equations (with C. Yu). J. Differential Equations 259 (2015), no. 8, 3976-4008.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF Linear stability of compressible vortex sheets in two-dimensional elastodynamics (with M. Chen, J. Hu). Adv. Math. 311 (2017), 18-60.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF Linear stability of compressible vortex sheets in 2D elastodynamics: variable coefficients (with M. Chen, J. Hu). Math. Ann. 376 (2020), 863-912.   PDF 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.   PDF Global regularity of the three-dimensional fractional micropolar equations (with J. Wu, Z. Ye). J. Math. Fluid Mech. 22 (2020), no. 2, 28.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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.   PDF 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. PDF 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.   PDF Inviscid limit of compressible viscoelastic equations with the no-slip boundary condition (with F. Xie). J. Differential Equations 353 (2023), 63-113.   PDF 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 Vanishing viscosity limit of compressible viscoelastic equations in half space (with X. Gu and F. Xie). J. Differential Equations 398 (2024), 319-343.   PDF BACK TO RESEARCH PAGE