Research Areas

Well-posedness, Regularity and Vanishing Viscosity limits on the Fluid dynamicequations arising in mathematical physics, including:

1. Navier-Stokesand Euler equations;

2. Boussinesq system;

3. Magnetohydrodynamics (MHD).

Publications

1. Y. Wang, X. Mei, J. Liu*, Hölder regularity in time of solutions to the generalized surface quasi-geostrophic equation, Appl. Math. Lett. 137 (2023), Paper No. 108480, 7 pp.

2. Y. Li, J. Liu*, Y. Wu, Global well-posedness of inviscid lake equations in the Besov spaces, Math. Methods Appl. Sci. 45 (2022), no. 16, 9545 –9559.

3. S. Wang, W. Xu, J. Liu*, Global well-posedness and large time behavior to 2D Boussinesq equations for MHD convection, Methods Appl. Anal. 29 (2022), no. 1, 31-56.

4. S. Wang, W. Xu, J. Liu*, Random polygons and optimal extrapolation estimates of ∏, Stat. Optim. Inf. Comput. 9 (2021), no. 1, 241-249.

5. S. Wang, W. Xu, J. Liu*, Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity, Z. Angew. Math. Phys. 72 (2021), no. 3, Paper No. 103, 23 pp.

6. Q. Jiu, J. Liu*, D. Niu, Global existence of weak solutions to the incompressible axisymmetric Euler equations without swirl, J. Nonlinear Sci. 31 (2021), no. 2, Paper No. 36, 24 pp.

7. S. Wang, Y. Wang, J. Liu*, Regularity criteria to the incompressible axisymmetric Boussinesq equations, Appl. Math. Lett. 112 (2021), Paper No. 106800, 7 pp.

8. J. Liu*, W. Xu, Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane, Nonlinear Anal. Real World Appl. 49 (2019), 355-367.

9. J. Liu*, S. Wang, Initial-boundary value problem for 2D micropolar equations without angular viscosity, Commun. Math. Sci. 16 (2018), no. 8, 617-633.

10. J. Liu, W. Wang*, Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations, J. Differential Equations 264 (2018), no. 3, 2351–2376.

11. Q. Jiu, J. Liu*, Regularity criteria to the 3D axisymmetric incompressible Magneto-hydrodynamics equations, Dyn. Partial Differ. Equ. 15 (2018), no. 2, 109–126.

12. D. Bian, J. Liu*, Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects, J. Differential Equations 263 (2017), no. 12, 8074–8101.

13. Q. Jiu, J. Liu*, J. Wu, H. Yu, On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation, Z. Angew. Math. Phys. 68 (2017), no. 5, Art. 107, 24 pp.

14. C. Chen, J. Liu*, Global well-posedness of 2D nonlinear Boussinesq equations with mixed partial viscosity and thermal diffusivity, Math. Methods Appl. Sci. 40 (2017), no. 12, 4412 –4424.

15. J. Liu*, D. Niu, Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry, Z. Angew. Math. Phys. 68 (2017), no. 3, Art. 69, 12 pp.

16. J. Liu*, On the initial boundary value problem for certain 2D MHD-alpha equations without velocity viscosity, Commun. Pure Appl. Anal. 15 (2016), no. 4, 1179–1191.

17. J. Liu*, On regularity criterion to the 3D axisymmetric incompressible MHD equations, Math. Methods Appl. Sci. 39 (2016), no. 15, 4535–4544.

18. Q. Jiu, J. Liu*, Global-wellposedness of 2D Boussinesq equations with mixed partial temperature-dependent viscosity and thermal diffusivity, Nonlinear Anal. 132 (2016), 227–239.

19. Q. Jiu, J. Liu*, Global regularity for the 3D axisymmetric MHD equations with horizontal dissipation and vertical magnetic diffusion, Discrete Contin. Dyn. Syst. 35 (2015), no. 1, 301–322.