Scholars@Duke

• Background
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  Education, Training, & Certifications

  • Ph.D., University of Illinois 2020
• Expertise
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  Subject Headings

  • Differential equations, Partial
  • Generalized solutions of partial differential equations
  • Partial differential equations
• Publications & Artistic Works
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  Selected Publications

  • Academic Articles

    • Kiselev, A., and X. Luo. “On Nonexistence of Splash Singularities for the α -SQG Patches.” Journal of Nonlinear Science 33, no. 2 (April 1, 2023). https://doi.org/10.1007/s00332-023-09893-2.
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    • Cheskidov, A., and X. Luo. “Sharp nonuniqueness for the Navier–Stokes equations.” Inventiones Mathematicae 229, no. 3 (September 1, 2022): 987–1054. https://doi.org/10.1007/s00222-022-01116-x.
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    • Kiselev, Alexander, and Xiaoyutao Luo. “On nonexistence of splash singularities for the $α$-SQG patches,” November 26, 2021.
       Link to Item
    • Cheskidov, A., and X. Luo. “Nonuniqueness of Weak Solutions for the Transport Equation at Critical Space Regularity.” Annals of Pde 7, no. 1 (June 1, 2021). https://doi.org/10.1007/s40818-020-00091-x.
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    • CHESKIDOV, A., and X. LUO. “Anomalous dissipation, anomalous work, and energy balance for the navier-stokes equations.” Siam Journal on Mathematical Analysis 53, no. 4 (January 1, 2021): 3856–87. https://doi.org/10.1137/20M1354076.
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    • Cheskidov, Alexey, and Xiaoyutao Luo. “Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces.” Nonlinearity 33, no. 4 (April 1, 2020): 1388–1403. https://doi.org/10.1088/1361-6544/ab60d3.
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    • Luo, Xiaoyutao. “On the possible time singularities for the 3D Navier–Stokes equations.” Physica D: Nonlinear Phenomena 395 (August 2019): 37–42. https://doi.org/10.1016/j.physd.2019.02.008.
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    • Luo, Xiaoyutao. “Stationary Solutions and Nonuniqueness of Weak Solutions for the Navier–Stokes Equations in High Dimensions.” Archive for Rational Mechanics and Analysis 233, no. 2 (August 2019): 701–47. https://doi.org/10.1007/s00205-019-01366-9.
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    • Luo, Xiaoyutao. “A Beale–Kato–Majda Criterion with Optimal Frequency and Temporal Localization.” Journal of Mathematical Fluid Mechanics 21, no. 1 (March 2019). https://doi.org/10.1007/s00021-019-0411-z.
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  • Preprints

    • Kiselev, Alexander, and Xiaoyutao Luo. “Illposedness of $C^{2}$ vortex patches,” April 13, 2022.
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• Teaching & Mentoring
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  Recent Courses

  • MATH 202D: Multivariable Calculus for Economics 2023
  • MATH 202D: Multivariable Calculus for Economics 2022
  • MATH 212D: Multivariable Calculus 2021
  • MATH 712D: Multivariable Calculus 2021

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