基本介紹
- 中文名：曾惠慧
- 畢業院校：香港中文大學
- 主要成就：2010年香港數學會最佳論文獎
2015年清華大學學術新人獎
2018年國家自然科學基金優秀青年基金 - 職稱：教授
人物經歷,教育背景,工作經歷,榮譽獎勵,研究領域,
1999-2003 學士 四川大學
2004-2009 博士 香港中文大學
2019.06-，清華大學丘成桐數敬少民學中心/數學系，教授
2012-2019，清華大學丘成桐數鍵捆紙學中心/數學系，副教授
2014-2015，美國哈佛大學，博士後茅乘蒸連
2009-2012，美國喬治城大學，博士後
2018年 國家自然科學基金優秀青年基金
2015年 清華大學學術新人獎
2010年 香港數學會最佳論文獎
曾惠慧的研究領域為非線性偏微分方程。她對於三維可壓縮Euler（或Euler-Poisson）方程物理真空自由界面問題，證明了古典解的無條件唯一性，並在新的泛函空間對球對稱運動建立了局部適定性；對於帶阻尼的可壓縮Euler方程物理真空自由界面問題，證明了整體光滑解的存在性及Barenblatt自相似解的非線性漸近穩定性；對於粘性氣狀星體物理真空自由界面問題，證明了球對稱整體強解的匪地舉存在性及著名Lane-Emden解的非線性漸近穩定性；對於流體力學及分子動力學方程如轎危Navier-Stokes方程和Boltzmann方兆驗墓程等在一些物理參數（如粘性、熱傳姜市茅懂導及平均自由程等）趨於零及時間趨於無窮大時，證明了解的漸近行為。
- 發表論文
[1] T. Luo and H. Zeng, On the free surface motion of highly subsonic heat-conducting inviscid flows, arXiv:1709.06925.
[2] H. Zeng, Global Resolution of the Physical Vacuum Singularity for 3-D Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions,Arch. Ration. Mech. Anal.226(2017),33-82.
[3] T. Luo and H. Zeng, Global existence of smooth solutions and convergence to Barenblatt solutions for the physical vacuum free boundary problem of compressible Euler equations with damping,Comm. Pure Appl. Math.69 (2016), 1354-1396.
[4] T. Luo, Z. Xin and H. Zeng, Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities,Comm. Math. Phy.347 (2016), 657-702.
[5] T. Luo, Z. Xin and H. Zeng, On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem,Adv. Math.291 (2016), 90-182.
[6] B. Yang and H. Zeng, Zero relaxation limit to rarefaction waves for general 2*2 hyperbolic systems with relaxation,Comm. Math. Sci.14 (2016), 443-462.
[7] Y. Ou and H. Zeng, Global strong solutions to the vacuum free boundary problem for compressible Navier-Stokes equations with degenerate viscosity and gravity force,J. Differential Equations259 (2015), 6803-6829.
[8] H. Zeng, Global smooth solutions of the vacuum free boundary problem for compressible isentropic Navier-Stokes equations,Nonlinearity28 (2015), 331-345.
[9] T. Luo, Z. Xin and H. Zeng, Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation,Arch. Ration. Mech. Anal.213 (2014), 763-831.
[10] J. Miller and H. Zeng, Range limits in spatially explicit models of quantitative traits,J. Math. Biol., 68 (2014), 207-234.
[11] H. Zeng, Stability of planar traveling waves for bistable reaction-diffusion equations in multiple dimensions,Appl. Anal.93 (2014), 653-664.
[12] H. Zeng, Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations,Sci. China Math.57 (2014), 353-366.
[13] J. Miller and H. Zeng, Multidimensional stability of planar traveling waves for an integrodifference model,Discrete Contin. Dyn. Syst. Ser. B18 (2013), 741-751.
[14] J. Miller and H. Zeng, Stability of travelling waves for systems of nonlinear integral recursions in spatial population biology,Discrete Contin. Dyn. Syst. Ser. B16 (2011), 895-925.
[15] H. Zeng, A class of initial value problems for 2*2 hyperbolic systems with relaxation,J. Differential Equations251 (2011), 1254-1275.
[16] Z. Xin and H. Zeng, Pointwise stability of contact discontinuity for viscous conservation laws with general perturbation,Comm. Partial Differential Equations35 (2010), 1326-1354.
[17] Z. Xin and H. Zeng, Convergence to rarefaction waves for Boltzmann equation and Compressible Navier-Stokes equations,J. Differential Equations249 (2010), 827-871.
[18] H. Zeng, Stability of a superposition of shock waves with contact discontinuities for systems of viscous conservation laws,J. Differential Equations246 (2009), 2081-2102.
[4] T. Luo, Z. Xin and H. Zeng, Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities,Comm. Math. Phy.347 (2016), 657-702.
[5] T. Luo, Z. Xin and H. Zeng, On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem,Adv. Math.291 (2016), 90-182.
[6] B. Yang and H. Zeng, Zero relaxation limit to rarefaction waves for general 2*2 hyperbolic systems with relaxation,Comm. Math. Sci.14 (2016), 443-462.
[7] Y. Ou and H. Zeng, Global strong solutions to the vacuum free boundary problem for compressible Navier-Stokes equations with degenerate viscosity and gravity force,J. Differential Equations259 (2015), 6803-6829.
[8] H. Zeng, Global smooth solutions of the vacuum free boundary problem for compressible isentropic Navier-Stokes equations,Nonlinearity28 (2015), 331-345.
[9] T. Luo, Z. Xin and H. Zeng, Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation,Arch. Ration. Mech. Anal.213 (2014), 763-831.
[10] J. Miller and H. Zeng, Range limits in spatially explicit models of quantitative traits,J. Math. Biol., 68 (2014), 207-234.
[11] H. Zeng, Stability of planar traveling waves for bistable reaction-diffusion equations in multiple dimensions,Appl. Anal.93 (2014), 653-664.
[12] H. Zeng, Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations,Sci. China Math.57 (2014), 353-366.
[13] J. Miller and H. Zeng, Multidimensional stability of planar traveling waves for an integrodifference model,Discrete Contin. Dyn. Syst. Ser. B18 (2013), 741-751.
[14] J. Miller and H. Zeng, Stability of travelling waves for systems of nonlinear integral recursions in spatial population biology,Discrete Contin. Dyn. Syst. Ser. B16 (2011), 895-925.
[15] H. Zeng, A class of initial value problems for 2*2 hyperbolic systems with relaxation,J. Differential Equations251 (2011), 1254-1275.
[16] Z. Xin and H. Zeng, Pointwise stability of contact discontinuity for viscous conservation laws with general perturbation,Comm. Partial Differential Equations35 (2010), 1326-1354.
[17] Z. Xin and H. Zeng, Convergence to rarefaction waves for Boltzmann equation and Compressible Navier-Stokes equations,J. Differential Equations249 (2010), 827-871.
[18] H. Zeng, Stability of a superposition of shock waves with contact discontinuities for systems of viscous conservation laws,J. Differential Equations246 (2009), 2081-2102.
