Projects per year
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
Research area keywords
- Nonlinear dispersive equation
- Navier-Stokes equation
- scattering theory
- well-posedness
- Stability
Network
Projects
- 2 Finished
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Nonlinear harmonic analysis and dispersive partial differential equations
Sikora, A., Guo, Z., Hauer, D. & Tacy, M.
8/04/20 → 31/12/22
Project: Research
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Harmonic analysis and dispersive partial differential equations
Guo, Z., Li, J., Kenig, C. & Nakanishi, K.
Australian Research Council (ARC), Monash University, Macquarie University, University of Chicago, Osaka University
1/01/17 → 1/11/20
Project: Research
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Generalized singular integral with rough kernel and approximation of surface quasi-geostrophic equation
Chen, Y. & Guo, Z., 15 Feb 2023, In: Journal of Differential Equations. 346, p. 205-228 24 p.Research output: Contribution to journal › Article › Research › peer-review
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Well-posedness of the modified dispersion-generalized Benjamin-Ono equations in modulation spaces
Guo, Z. & Huang, C., 1 May 2022, In: Journal of Mathematical Analysis and Applications. 509, 1, 20 p., 125933.Research output: Contribution to journal › Article › Research › peer-review
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An extension of Calderón-Zygmund type singular integral with non-smooth kernel
Chen, Y. & Guo, Z., 1 Nov 2021, In: Journal of Functional Analysis. 281, 9, 21 p., 109196.Research output: Contribution to journal › Article › Research › peer-review
Open Access1 Citation (Scopus) -
Commutators of Hilbert transforms along monomial curves
Bongers, T., Guo, Z., Li, J. & Wick, B. D., 2021, In: Studia Mathematica. 257, 3, p. 295-311 17 p.Research output: Contribution to journal › Article › Research › peer-review
2 Citations (Scopus) -
Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces
Guo, Z. & Li, K., Apr 2021, In: Journal of Fourier Analysis and Applications. 27, 2, 24 p., 29.Research output: Contribution to journal › Article › Research › peer-review
Open Access2 Citations (Scopus)