27. Jia, H., Yuan, C., Lei, Z., Sharp Asymptotic Stability of Blasius Profile in the Steady Prandtl Equation, arXiv:2408.13747
(This work establishes the sharp rate of convergence of general solutions, without any size restrictions, to Blasius self similar solutions of the steady Prandtl equation when $x\to\infty$.)
26. Beekie, R., Chen, S., Jia, H., Uniform vorticity depletion and inviscid damping for periodic shear flows in the high Reynolds number regime, arXiv:2403.13104
(In this paper, we studied the interaction of vorticity depletion, inviscid damping and viscosity, uniformly in the limit $\nu\to0+$; and established the almost sharp rate of vorticity depletion near the critical points of the background shear flow. Highlight includes a new perspective in solving the Orr-Sommerfeld equation for full range of spectral parameters, without the use of specific ODE techniques or special functions. See https://drive.google.com/file/d/1Sawjv8hUb8FgyjXYixyU1BGnakpLQSHe/view?usp=drive_link for a numerical simulation for the linearized NSE around Kolmogorov at a fixed x-frequency, where the viscosity is 1e-7. The simulation shows the vorticity depletion effect at the critical points as well enhanced dissipation. Moreover, the rates of decay for vorticity away from the critical points are faster than that around the critical points. Compare this with the simulation https://drive.google.com/file/d/1ct9H_ehZQshnYe7ep39Qmz9uaj61iI-B/view?usp=drive_link for the diffusion-transport equation having the same viscosity and initial data. It is clear that the nonlocal term in the linearized NSE accelerates the decay of vorticity.)
25. Jia, H., Remarks on the rate of linear vortex symmetrization, arXiv:2403.09397
(In this short note, we reformulate the result from arXiv:2109.12815 to rigorously justify the predictions of Bassom and Gilbert, J.Fluid.Mech. 1998, on the rate of linear vortex symmetrization near smooth monotonic vortices.)
24. Ionescu, A., Iyer, S., Jia, H., Linear inviscid damping and vorticity depletion for non-monotonic shear flows, arXiv:2301.00288
23. Jia, H., Uniform linear inviscid damping and enhanced dissipation near monotonic shear flows in high Reynolds number regime (I): the whole space case, Journal of Mathematical Fluid Mechanics, Vol. 25, article no. 42, 2023, arXiv:2207.10987
22. Ionescu, A.D., Jia, H., Linear vortex symmetrization: the spectral density function, Archive for Rational Mechanics and Analysis 246 (1), 61-137, 2022, arXiv:2109.12815
21. Ionescu, A.D., Jia, H., Nonlinear inviscid damping near monotonic shear flows, Acta Mathematica 230 (2), 321-399, 2023, arXiv:2001.03087
20. Ionescu, A.D., Jia, H., Axi-symmetrization near point vortex solutions for the 2D Euler equation, Comm.Pure Appl. Math., 75 (4), 818-891, 2022, arXiv 1904.09170
19. Jia, H., Linear Inviscid Damping in Gevrey Spaces, Archive for Rational Mechanics and Analysis, 235, 1327–1355 (2020), arXiv:1904.01188
18. Jia, H., Linear Inviscid damping near monotone shear flows, SIAM J. Math. Anal., 52 (1), 623-652, arXiv:1902.06849
17. Ionescu, A.D., Jia, H., Inviscid Damping Near the Couette Flow in a Channel, Comm. Math. Phys., 339 (2), 353-384. arXiv:1808.04026
16. Jia, H., Šverák, V., Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions, Acta. Math. Sin. English Ser. 34, 598–611 (2018), https://doi.org/10.1007/s10114-017-7397-3
15. Jia, H., Stewart, S., Sverak, V., On the De Gregorio Modification of the Constantin–Lax–Majda Model, Archive for Rational Mechanics and Analysis, 231, 1269–1304 (2019). https://doi.org/10.1007/s00205-018-1298-1, arXiv:1710.02737
14. Jia, H., Liu, B., Schlag, W., Xu, G., Global center stable manifold for the defocusing energy critical wave equation with potential, American Journal of Mathematics, 142 (5), 1497-1557, arXiv:1706.09284
13. Duyckaerts, T., Jia, H., Kenig, C., Merle, F., Universality of Blow up Profile for Small Blow up Solutions to the Energy Critical Wave Map Equation, International Mathematics Research Notices, Volume 2018, Issue 22, November 2018, Pages 6961–7025, https://doi.org/10.1093/imrn/rnx073. arXiv:1612.04927
12. Duyckaerts, T., Jia, H., Kenig, C. Merle, F., Soliton resolution along a sequence of times for the focusing energy critical wave equation, Geometric and Functional Analysis, Vol. 27, 798–862 (2017). https://doi.org/10.1007/s00039-017-04187. arXiv:1601.01871
*This paper is an extension of arXiv:1510.00075, in two ways: 1) the global case is now considered, 2) significantly the dispersive error is now shown to vanish asymptotically in energy space.
11. Jia, H., Soliton resolution along a sequence of times with dispersive error for type II singular solutions to focusing energy critical wave equation, preprint 2015, 42 pages, arXiv:1510.00075
10. Jia, H., Liu, B., Schlag, W., Xu, G., Generic and Non-Generic Behavior of Solutions to Defocusing Energy Critical Wave Equation with Potential in the Radial Case, International Mathematics Research Notices, Volume 2017, Issue 19, October 2017, Pages 5977–6035, https://doi.org/10.1093/imrn/rnw181. arXiv 1506.04763
9. Jia, H., Kenig, C., Asymptotic decomposition for semilinear Wave and equivariant wave map equations, American Journal of Mathematics, vol. 139 no. 6, 2017, p. 1521-1603. Project MUSE, doi:10.1353/ajm.2017.0039. arXiv:1503.06715
8. Jia, H., Uniqueness of solutions to to Navier Stokes equation with small initial data in $L^{3,infty}(R^3)$, preprint 2014. arXiv:1409.8382
7. Jia, H., Liu, B., Xu, G., Long Time Dynamics of Defocusing Energy Critical 3 + 1 Dimensional Wave Equation with Potential in the Radial Case, Comm. Math. Phys. 339, 353–384 (2015). https://doi.org/10.1007/s00220-015-2422-9. arXiv:1403.5696
6. Jia, H., Šverák, V., Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?, Journal of Functional Analysis, 268. 10.1016/j.jfa.2015.04.006. arXiv:1306.2136
5. Jia, H., Šverák, V., Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions, Inventiones Mathematicae, 196, 233–265 (2014). https://doi.org/10.1007/s00222-013-0468-x. arXiv:1204.0529
4. Jia, H., Seregin, G., Šverák, V., Liouville theorems in unbounded domains for the time-dependent Stokes system, Journal of Mathematical Physics, 53. 10.1063/1.4738636. arXiv:1201.1664
3. Jia, H., Sverák, V., Minimal L3-Initial Data for Potential Navier-Stokes Singularities, SIAM J.Math.Analysis, 45 (2013): 1448-1459. arXiv:1201.1592
2. Jia, H., Sverák, V., On scale-invariant solutions of the Navier–Stokes equations, Proceedings of the 6th European Congress of Mathematicians (2012) .
1. Jia, H., Seregin, G., Sverak, V., A Liouville theorem for the Stokes system in a half-space, J. Math. Sci, 195, 13–19 (2013). https://doi.org/10.1007/s10958-013-1561-9