Records in Databases:   MathSciNet    Scopus    Web of Science

Preprints (arXiv)

[1] M. Abatangelo, C. Cavaterra, M. Grasselli and Hao Wu, Optimal distributed control for a Cahn–Hilliard–Darcy system with mass sources, unmatched viscosities and singular potential, preprint, 2023. [arXiv]

[2] C. Gal, M-.Y. Lv and H. Wu, On a thermodynamically consistent diffuse interface model for two-phase incompressible flows with non-matched densities: Dynamics of moving contact lines, surface diffusion, and mass transfer, preprint, 2024. [link]

[3] M-.Y. Lv and H. Wu, On the Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions and non-smooth potentials: Well-posedness and asymptotic limits, preprint, 2024. [arXiv]

Articles in Refereed Journals

2024

• Hao Wu and S.-Q. Xu, Well-posedness and long-time behavior of a bulk-surface coupled Cahn–Hilliard–diffusion system with singular potential for lipid raft formation, Discrete Contin. Dyn. Syst. Ser. S, 17(1) (2024), 1–61. [arXiv]
  

• J.-N. He and Hao Wu, On a Navier–Stokes–Cahn–Hilliard system for viscous incompressible two-phase flows with chemotaxis, active transport and reaction, Math. Ann., online first, 2023. https://doi.org/10.1007/s00208-023-02701-y [link]

2023

• W.-B. Chen, J.-Y. Jing and Hao Wu, A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn–Hilliard equation with logarithmic potential, J. Sci. Comput., 96(3) (2023), Article number: 75, 45 pages. [link]
  

• A. Di Primio, M. Grasselli and Hao Wu, Navier–Stokes–Cahn–Hilliard System for incompressible two-phase flows with surfactant, Math. Models Methods Appl. Sci., 33(4) (2023), 755–828. [arXiv]

• F. De Anna and Hao Wu, Uniqueness of weak solutions for the general Ericksen–Leslie system with Ginzburg–Landau penalization in T^2, Calc. Var. Partial Differential Equations, 62 (2023), Article number: 157, 79 pages. [link]

2022

• A. Giorgini, M. Grasselli and Hao Wu, On the mass-conserving Allen–Cahn approximation for incompressible binary fluids, J. Funct. Anal., 283(9) (2022), article no. 109631, 86 pages.  [arXiv]
  

• Hao Wu and Y.-C. Yang, Well-posedness of a hydrodynamic phase-field model for functionalized membrane-fluid interaction, Discrete Contin. Dyn. Syst. Ser. S, 15(8) (2022), 2345–2389. [arXiv]
  

• Hao Wu, A review on the Cahn–Hilliard equation: classical results and recent advances in dynamic boundary conditions, Electron. Res. Arch., 30(8) (2022), 2788–2832. [link]
  

2021

• T. Fukao and Hao Wu, Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential, Asymptotic Anal., 124(3-4) (2021), 303-341. [arXiv]

• J.-N. He and Hao Wu, Global well-posedness of a Navier–Stokes–Cahn–Hilliard system with chemotaxis and singular potential in 2D, J. Differential Equations, 297 (2021), 47–80. [arXiv]

• C. Cavaterra, E. Rocca and Hao Wu, Long-time dynamics and optimal control of a diffuse interface model for tumor growth, Appl. Math. Optim., 83(2) (2021), 739–787. [link]

• J. Sprekels and Hao Wu, Optimal distributed control of a Cahn–Hilliard–Darcy system with mass sources, Appl. Math. Optim., 83(1) (2021), 489–530. [link]

• X.-M. Wang and Hao Wu, Global weak solutions to the Navier–Stokes–Darcy–Boussinesq system for thermal convection in coupled free and porous media flows, Adv. Differential Equations, 26(1&2) (2021), 1–44. [arXiv]

2020

• P. Colli, T. Fukao and Hao Wu, On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials, Math. Nachr., 293(11) (2020), 2051–2081. [link]

• G. Schimperna and Hao Wu, On a class of sixth-order Cahn–Hilliard type equations with logarithmic potential, SIAM J. Math. Anal., 52(5) (2020), 5155–5195. [arXiv]

• A. Miranville and Hao Wu, Long-time behavior of the Cahn–Hilliard equation with dynamic boundary condition, J. Elliptic Parabol. Equ., 6(1) (2020), 283–309.  [link]

• E. Espejo and Hao Wu, Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms, Commun. Math. Sci., 18(2) (2020), 379–394.

• K.-F. Lam and Hao Wu, Convergence to equilibrium for a bulk-surface Allen–Cahn system coupled through a nonlinear Robin boundary condition, Discrete Contin. Dyn. Syst., 40(3) (2020), 1847–1878.  [arXiv]

2019

• Y.-N. Liu, Hao Wu and X. Xu, Global well-posedness of the two dimensional Beris–Edwards system with general Laudau–de Gennes free energy, J. Differential Equations, 267(12) (2019), 6958–7001. [arXiv]

• C. Gal, M. Grasselli and Hao Wu, Global weak solutions to a diffuse interface model for  incompressible two-phase flows with moving contact lines and different densities, Arch. Rational Mech. Anal., 234(1) (2019), 1–56. [link]

• C. Liu and Hao Wu, An energetic variational approach for the Cahn–Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis, Arch. Rational Mech. Anal., 233(1) (2019), 167–247. [link]

• Hao Wu, X. Xu and A. Zarnescu, Dynamics and flow effects in the Beris–Edwards system modeling nematic liquid crystals, Arch. Rational Mech. Anal., 231(2) (2019), 1217–1267. [link]

2018

• K.-F. Lam and Hao Wu, Thermodynamically consistent Navier–Stokes–Cahn–Hilliard models with mass transfer and chemotaxis, European J. Appl. Math., 29(4) (2018), 595–644. [arXiv]

• A. Giorgini, M. Grasselli and Hao Wu, The Cahn–Hilliard–Hele–Shaw system with singular potential, Ann. Inst. H. Poincare Anal. Non Lineaire, 35(4) (2018), 1079–1118. [HAL]

• J. Jiang, Hao Wu and S. Zheng, Blow-up for a three dimensional Keller–Segel model with consumption of chemoattractant, J. Differential Equations, 264(8) (2018), 5432–5464. [arXiv]

2017

• C. Cavaterra, E. Rocca and Hao Wu, Optimal boundary control of a simplified Ericsken–Leslie system for incompressible liquid crystal flows in 2D, Arch. Rational Mech. Anal., 224(3) (2017), 1037–1086. [link]

• Hao Wu, Well-posedness of a diffuse-interface model for two-phase incompressible flows with thermo-induced Marangoni effect, European J. Appl. Math., 28(3) (2017), 380–434. [arXiv]

2016

• C. Cavaterra, E. Rocca, Hao Wu and X. Xu, Global strong solutions of the full Navier–Stokes and Q-tensor system for incompressible nematic liquid crystal flows in two dimensions, SIAM J. Math. Anal., 48(2) (2016), 1368–1399. [arXiv]

2015

• J. Jiang, Hao Wu and S. Zheng, Well-posedness and long-time behavior of a non-autonomous Cahn–Hilliard–Darcy system with mass source modeling tumor growth, J. Differential Equations, 259(7) (2015), 3032–3077. [arXiv]

• X.-P. Hu and Hao Wu, Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35(8) (2015), 3437–3461. [arXiv]

• Hao Wu, T.-C. Lin and C. Liu, Diffusion limit of kinetic equations for multiple species charged particles, Arch. Rational Mech. Anal., 215(2) (2015), 419–441. [link]

• J. Jiang, Hao Wu and S. Zheng, Global Solutions to a chemotaxis-fluid system on general bounded domain, Asymptotic Anal., 92(3&4) (2015), 249–258. [arXiv]

• M. Grasselli and Hao Wu, Robust exponential attractors for the modified phase-field crystal equation, Discrete Contin. Dyn. Syst., 35(6) (2015), 2539–2564. [arXiv]

2014

• M. Grasselli and Hao Wu, Well-posedness and long-time dynamics of the modified phase-field crystal equation, Math. Models Methods Appl. Sci., 24(14) (2014), 2743–2783. [arXiv]

• D.-Z. Han, X.-M. Wang and Hao Wu, Existence and uniqueness of global weak solutions to a Cahn–Hilliard–Stokes–Darcy system for two phase incompressible flows in karstic geometry, J. Differential Equations, 257(10) (2014), 3887–3933. [arXiv]

• M. Korzec and Hao Wu, Analysis and simulation for an isotropic phase-field model describing grain growth, Discrete Contin. Dyn. Syst. Ser. B, 19(7) (2014), 2227–2246.

• C. Cavaterra, M. Grasselli and Hao Wu, Non-isothermal viscous Cahn–Hilliard equation with inertial term and dynamic boundary conditions, Commun. Pure Appl. Anal., 13(5) (2014), 1855–1890. [arXiv]

2013

• Hao Wu and J. Jiang, Global solution to the drift-diffusion-Poisson system for semiconductors with nonlinear recombination-generation rate, Asymptotic Anal.,  85(1&2) (2013), 75–105. [arXiv]

• X.-P. Hu and Hao Wu, Global solution to the three-dimensional compressible flow of liquid crystals, SIAM J. Math. Anal., 45(5) (2013), 2678–2699. [arXiv]

• X.-P. Hu and Hao Wu, Long-time dynamics of a hydrodynamical system for inhomogeneous incompressible nematic liquid crystal flows, Commun. Math. Sci., 11(3) (2013), 779–806. [arXiv]

• M. Grasselli and Hao Wu, Long-time behavior for a nematic liquid crystal model with asymptotic stabilizing boundary condition and external force, SIAM J. Math. Anal., 45(3) (2013), 965–1002. [arXiv]

• C. Cavaterra, E. Rocca and Hao Wu, Global weak solution and blow criterion of the general Ericksen–Leslie system for nematic liquid crystal flows, J. Differential Equations, 255(1) (2013), 24–57. [arXiv]

• Hao Wu, X. Xu and C. Liu, On the general Ericksen–Leslie system: Parodi’s relation, well-posedness and stability, Arch. Rational Mech. Anal., 208(1) (2013), 59–107. [link]

• Hao Wu and X. Xu, Analysis of a diffuse-interface model for the mixture of two viscous incompressible fluids with thermo-induced Marangoni effects, Commun. Math. Sci., 11(2) (2013), 603–633. [arXiv]

• Hao Wu and X. Xu, Strong solutions, global regularity, and stability of a hydrodynamical system modeling vesicle and fluid interactions, SIAM J. Math. Anal., 45(1) (2013), 181–214. [arXiv]

2012

• Hao Wu, X. Xu and C. Liu, Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties, Calc. Var. Partial Differential Equations,  45(3&4) (2012), 319–345. [link]

• Hao Wu and M. Wunsch, Global existence for the generalized two-component Hunter–Saxton system, J. Math. Fluid Mech., 14(3) (2012), 455–469. [link]

• X.-M. Wang and Hao Wu, Long-time behavior for the Hele–Shaw–Cahn–Hilliard system, Asymptotic Anal., 78(4) (2012), 217–245.

• J. Jiang, Hao Wu and B.-L. Guo, Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg–Landau equations, Sci. China Math., 55(1) (2012), 141–157. [link]

2011

• M. Grasselli and Hao Wu, Finite-dimensional global attractor for a system modeling the 2D nematic liquid crystal flow, Z. Angew. Math. Phys., 62(6) (2011), 979–992. [link]

• A. Segatti and Hao Wu, Finite dimensional reduction and convergence to equilibrium for incompressible Smectic-A liquid crystal flows, SIAM J. Math. Anal., 43(6) (2011), 2445–2481.

2010

• J. Sprekels and Hao Wu, A note on parabolic equation with nonlinear dynamical boundary condition, Nonlinear Anal. TMA, 72(6) (2010), 3028–3048.

• Hao Wu, Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows, Discrete Contin. Dyn. Syst., 26(1) (2010), 379–396. [arXiv]

2009

• L.-Y. Zhao, Hao Wu and H.-Y. Huang, Convergence to equilibrium for a phase-field model for the mixture of two incompressible fluids, Commun. Math. Sci., 7(4) (2009), 939–962.

• M. Grasselli, Hao Wu and S. Zheng, Convergence to equilibrium for parabolic-hyperbolic time-dependent Ginzburg–Landau–Maxwell equations, SIAM J. Math. Anal., 40(5) (2009), 2007–2033.

2008

• M. Grasselli, Hao Wu and S. Zheng, Asymptotic behavior of a non-isothermal Ginzburg–Landau model, Quart. Appl. Math., 66(4) (2008), 743–770.

• Hao Wu, Long-time behavior for a nonlinear plate equation with thermal memory, J. Math. Anal. Appl., 348(2) (2008), 650–670. [arXiv]

• C. Gal and Hao Wu, Asymptotic behavior of a Cahn–Hilliard equation with Wentzell boundary conditions and mass conservation, Discrete Contin. Dyn. Syst., 22(4) (2008), 1041–1063.

• Hao Wu, P. A. Markowich and S. Zheng, Global existence and asymptotic behavior for a semiconductor drift-diffusion-Poisson model, Math. Models Methods Appl. Sci., 18(3) (2008), 443–487.

2007

• Hao Wu, Convergence to equilibrium for a Cahn–Hilliard model with the Wentzell boundary condition, Asymptotic Anal., 54(1&2) (2007), 71–92. [arXiv]

• Hao Wu, Convergence to equilibrium for the semilinear parabolic equation with dynamical boundary condition, Adv. Math. Sci. Appl., 17(1) (2007), 67–88. [arXiv]

• Hao Wu and S. Zheng, Global attractor for the 1-d thin film equation, Asymptotic Anal., 51(2) (2007), 101–111.

• Hao Wu, M. Grasselli and S. Zheng, Convergence to equilibrium for a nonlinear parabolic-hyperbolic phase-field system with dynamical boundary condition, J. Math. Anal. Appl., 329(2) (2007), 948–976.

• Hao Wu, M. Grasselli and S. Zheng, Convergence to equilibrium for a parabolic-hyperbolic phase-field system with Neumann boundary conditions, Math. Models Methods Appl. Sci., 17(1) (2007), 1–29.

2006

• Hao Wu and S. Zheng, Convergence to equilibrium for the damped semilinear wave equation with critical exponent and dissipative boundary condition, Quart. Appl. Math., 64(1) (2006) 167–188.

2004

• Hao Wu and S. Zheng, Convergence to equilibrium for the Cahn–Hilliard equation with dynamic boundary conditions, J. Differential Equations, 204(2) (2004), 511–531.  

Articles in Conference Proceedings

[1] Hao Wu, The Cahn-Hilliard equation with a new class of dynamic boundary conditions, RIMS Kokyuroku, No. 2090, pp. 117–131, 2018.

[2] Hao Wu, Convergence to equilibrium for some nonlinear evolution equations with dynamical boundary condition, Proceedings in Applied Mathematics and Mechanics (PAMM), Vol. 7, Issue 1, pp. 2040061–2040062, 2007.

[3] Hao Wu and S. Zheng, Asymptotic behavior of solutions to the Cahn–Hilliard equation with dynamic boundary conditions, GAKUTO international Series, Math. Sci. Appl., Vol. 20, pp. 382–390, 2004.  

Unpublished Manuscripts

[1] P. Krejci, J. Sprekels and Hao Wu, Elastoplastic Timoshenko beams, WIAS preprint, No. 1430, 2009. [link]