Zihua Guo

Assoc Professor

Accepting PhD Students

20072019
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Personal profile

Biography

Research interests

Research interest: harmonic analysis and partial differential equations

Harmonic analysis: to study the boundedness in various function spaces for the linear/multilinear operators related to the Fourier restriction problem and PDEs, function spaces, space-time estimates for dispersive equations.

Nonlinear partial differential equation: to study the nonlinear evolutionary PDEs arising in mathematical physics such as nonlinear dispersive equations, Navier-Stokes equation.  Main concerns are the low-regularity local/global well-posedness theory, long-time/blow-up behavior of the solution, stability of the equation, playing tools from many other areas including harmonic analysis, functional analysis, ODE and probability, etc.

Harmonic analysis and PDEs

Keywords

  • Nonlinear dispersive equation
  • Navier-Stokes equation
  • scattering theory
  • well-posedness
  • Stability

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Projects 2017 2019

Research Output 2007 2019

Ill-posedness of the Camassa–Holm and related equations in the critical space

Guo, Z., Liu, X., Molinet, L. & Yin, Z., 15 Jan 2019, In : Journal of Differential Equations. 266, 2-3, p. 1698-1707 10 p.

Research output: Contribution to journalArticleResearchpeer-review

Local well-posedness of the incompressible Euler equations in B∞,1 1 and the inviscid limit of the Navier–Stokes equations

Guo, Z., Li, J. & Yin, Z., 1 May 2019, In : Journal of Functional Analysis. 276, 9, p. 2821-2830 10 p.

Research output: Contribution to journalArticleResearchpeer-review

Stability of peakons for the generalized modified Camassa–Holm equation

Guo, Z., Liu, X., Liu, X. & Qu, C., 2019, In : Journal of Differential Equations. 266, 12, p. 7749-7779 31 p.

Research output: Contribution to journalArticleResearchpeer-review

Lp Bilinear Quasimode Estimates

Guo, Z., Han, X. & Tacy, M., 1 Jan 2018, (Accepted/In press) In : Journal of Geometric Analysis. 48 p.

Research output: Contribution to journalArticleResearchpeer-review

Non-existence of solutions for the periodic cubic NLS below L2

Guo, Z. & Oh, T., 1 Mar 2018, In : International Mathematics Research Notices. 2018, 6, p. 1656-1729 74 p.

Research output: Contribution to journalArticleResearchpeer-review