Publications and Preprints
▪ Each preprint is the authors' version of a work that was submitted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. So please note that changes may have been made to this work since it was submitted for publication. To obtain a definitive version, one might visit the publishers' WebPages.
▪ If you are interested in our works, feel free to send emails to me for electronic preprints or reprints.
▪ ResearcherID: C-2160-2013
▪ MR Author ID: 729438
 A remark on mixed boundary value problem for Laplace equation, Acta Math. Sinica, Ser. A, 46(6)( 2003), 1091—1096 (in Chinese).
 Transonic shocks for steady Euler flows with cylindrical symmetry, Nonlinear Analysis, 66(8) (2007), 1853—1878. doi:10.1016/j.na.2006.02.045
 On transonic shocks in two dimensional variable-area ducts for steady Euler system, SIAM Journal of Mathematical Analysis, 38(4)(2006), 1343—1370. Click here for a pdf file.
 (with Shuxing Chen) Transonic shocks in compressible flow passing a duct for three-dimensional Euler system, Archive for Rational Mechanics and Analysis, 187(3) (2008), 523—556.
 A Remark on Determination of Transonic Shocks in Divergent Nozzles for Steady Compressible Euler Flows, Nonlinear Analysis: Real World Applications, 9(2008), 316—325. Click here for a pdf file.
[•] Thesis: On a class of transonic shocks in nozzles, Fudan University, 2006. (In Chinese)
 (with Li Liu) Stability of Cylindrical Transonic Shocks for Two-Dimensional Steady Compressible Euler System, Journal of Hyperbolic Differential Equations, 5(2)(2008), 347—379. Click here for a pdf file.
 Examples of Steady Subsonic Flows in a Convergent-Divergent Approximate Nozzle, Journal of Differential Equations, 244(7)(2008), 1675—1691. Click here for a pdf file.
 (with Yue He) Transonic Potential Flows in a Convergent-Divergent Approximate Nozzle, Journal of Mathematical Analysis and Applications, 353(2)(2009), 614—626. (Click to obtain preprint from arXiv)
 (with Gui-Qiang Chen) Uniqueness of Transonic Shock Solutions in a Duct for Steady Potential Flow, Journal of Differential Equations, 247(2)(2009), 564—573. (Click to obtain preprint from arXiv )
 (with Li Liu) Global Uniqueness of Transonic Shocks in Divergent Nozzles for Steady Potential Flows, SIAM Journal of Mathematical Analysis, 41(5)(2009), 1816—1824. (Click to obtain preprint from arXiv)
 (with Pan Liu) Uniqueness and Instability of Subsonic-Sonic Potential Flow in A Convergent Approximate Nozzle, Proceedings of American Mathematical Society, 138(5)(2010), 1793—1801. (Click to obtain preprint from arXiv)
 (with Beixiang Fang and Ya-Guang Wang) Reflection and refraction of shocks on an interface with a reflected rarefaction wave, Journal of Mathematical Physics, 52 (2011), no.7, 073702, 14 pages.
 (with Li Liu) Uniqueness of symmetric steady subsonic flows in infinitely long divergent nozzles, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 62(4)(2011), 641—647.
 Persistence of shocks in duct. Nonlinear Analysis, 75 (9) (2012), 3874– 3894.
 (with Beixiang Fang and Li Liu) Global Uniqueness of Transonic Shocks in Two-Dimensional Steady Compressible Euler Flows. Archive for Rational Mechanics and Analysis, 207(1)(2013), 317– 345. http://arxiv.org/abs/1004.2002
 (with Gui-Qiang Chen) Local Uniqueness of Steady Spherical Transonic Shock-fronts for the Three-Dimensional Full Euler Equations. Communications on Pure and Applied Analysis, 12(6) (2013), 2515–2542. http://arxiv.org/abs/1112.1750
 (with Gui-Qiang Chen and Vaibhav Kukreja) Stability of Transonic Contact Discontinuity in Two-Dimensional Steady Euler Flows. Journal of Mathematical Physics, 54 (2013), no.2, 021506, 24 pages.
 (with Gui-Qiang Chen and Vaibhav Kukreja) Well-posedness of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows. Zeitschrift für Angewandte Mathematik und Physik 64 (2013), no. 6, 1711–1727. http://arxiv.org/abs/1209.3806
 (with Li Liu) Steady Subsonic Potential Flows Through Infinite Multi-Dimensional Largely-Open Nozzles. Calculus of Variations and Partial Differential Equations. 49 (2014), no.1-2, 1–36.
 (with Ya-Guang Wang) Weak
Stability of Transonic Contact
Discontinuities in Three-Dimensional Steady Non-isentropic Compressible
Euler Flows. Zeitschrift für Angewandte
Mathematik und Physik.
66 (2015), no. 2, 341–388. Click
here for a preprint.
Vaibhav Kukreja; Hairong Yuan; Qiuju
Zhao: Stability of Transonic Jet with Strong Shock in Two-Dimensional Steady
Compressible Euler Flows. J. Differential Equations 258 (2015), no. 7, 2572–2617. Click here
for a preprint.
 Liu, Li; Xu, Meng; Yuan, Hairong. A mixed boundary value problem for Chaplygin’s hodograph equation. 423 (2015), no. 1, 60–75. (DOI: 10.1016/j.jmaa.2014.09.075)
 Xu, Meng; Liu, Li; Yuan, Hairong. On Tricomi problem of Chaplygin's hodograph equation. Abstr. Appl. Anal. 2015, Art. ID 754781, 11 pp.
 Liu, Li; Xu, Gang; Yuan, Hairong. Stability of Spherically Symmetric Subsonic Flows and Transonic Shocks under Multidimensional Perturbations. Adv. Math. 291 (2016), 696–757.
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