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Affiliation |
Graduate School of Engineering Science Department of Mathematical Science and Electrical-Electronic-Computer Engineering Mathematical Science Course |
DENG DINGQUN
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Research Interests 【 display / non-display 】
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kinetic theory, partial differential equations, Boltzmann equation, nonlinear analysis and boundary problems
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fluid dynamics, general relativistic and quantum kinetic equations
Graduating School 【 display / non-display 】
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2013.08-2017.06
Sun Yat-sen University Faculty of Science School of Mathematics Graduated
Graduate School 【 display / non-display 】
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2017.08-2021.07
City University of Hong Kong Graduate School, Division of Mathematics Department of Mathematics Doctor's Course Completed
Degree 【 display / non-display 】
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City University of Hong Kong - Doctor of Philosophy (PhD)
Campus Career 【 display / non-display 】
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2025.04-Now
Akita University Graduate School of Engineering Science Department of Mathematical Science and Electrical-Electronic-Computer Engineering Mathematical Science Course Associate Professor
External Career 【 display / non-display 】
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2023.08-2025.03
Pohang University of Science and Technology Research Assistant Professor
Research Areas 【 display / non-display 】
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Natural Science / Mathematical analysis
Research Achievements 【 display / non-display 】
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On the Cauchy problem of Boltzmann equation with a very soft potential
Dingqun Deng
Journal of Evolution Equations ( Springer Science and Business Media {LLC} ) 22 ( 1 ) 2022.03
Research paper (journal)
This work proves the global existence to Boltzmann equation in the whole space with very soft potential<i> γ</i> ∈ [0, <i>d</i>) and angular cutoff, in the framework of small perturbation of equilibrium state. In this article, we generalize the estimate on linearized collision operator <i>L</i> to the case of very soft potential and obtain the spectrum structure of the linearized Boltzmann operator correspondingly. The global classic solution can be derived by the method of strongly continuous semigroup. For soft potential, the linearized Boltzmann operator could not give spectral gap; hence, we have to consider a weighted velocity space in order to obtain algebraic decay in time.
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Regularity of the Vlasov–Poisson–Boltzmann System Without Angular Cutoff
Dingqun DENG
Communications in Mathematical Physics ( Springer ) 387 ( 3 ) 1603 - 1654 2021.11
Research paper (journal)
In this paper we study the regularity of the non-cutoff Vlasov–Poisson–Boltzmann system for plasma particles of two species in the whole space ℝ<sup>3</sup> with hard potential. The existence of global-in-time nearby Maxwellian solutions is known for soft potential from Duan and Liu (Commun Math Phys 324(1):1–45, 2013). However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to (<i>t</i>,<i> x</i>, <i>v</i>) for any positive time <i>t </i>> 0. This gives regularity to the Vlasov–Poisson–Boltzmann system, which enjoys a similar smoothing effect as the Boltzmann equation. The proof is based on the time-weighted energy method building also upon the pseudo-differential calculus.
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Smoothing estimates of the Vlasov-Poisson-Landau system
Dingqun Deng
Journal of Differential Equations ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 301 112 - 168 2021.11
Research paper (journal)
In this work, we consider the smoothing effect of Vlasov-Poisson-Landau system for both hard and soft potential. In particular, we prove that any classical solutions becomes immediately smooth with respect to all variables. We also give a proof on the global existence to Vlasov-Poisson-Landau system with optimal large time decay. These results give the regularity to Vlasov-Poisson-Landau system. The proof is based on the time-weighted energy method building upon the Pseudodifferential calculus.
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Regularity of Non-cutoff Boltzmann Equation with Hard Potential
Dingqun Deng
SIAM Journal on Mathematical Analysis ( Society for Industrial {\&} Applied Mathematics ({SIAM}) ) 53 ( 4 ) 4513 - 4536 2021.01
Research paper (journal)
This article proves the regularity for the Boltzmann equation without angular cutoff with hard potential. By sharpening the coercivity and upper bound estimate on the collision operator, analyzing the Poisson bracket between the transport operator and some weighted pseudodifferential operator, we prove the regularizing effect in space and velocity variables when the initial data have mild regularity.
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Dissipation and Semigroup on $H^k_n$: Non-cutoff Linearized Boltzmann Operator with Soft Potential
Dingqun Deng
SIAM Journal on Mathematical Analysis ( Society for Industrial {\&} Applied Mathematics ({SIAM}) ) 52 ( 3 ) 3093 - 3113 2020.01
Research paper (journal)
In this paper, we find that the linearized collision operator <i>L </i>of the non-cutoff
Boltzmann equation with soft potential generates a strongly continuous semigroup on <i>H<sup>k</sup><sub>n</sub></i>, with
<i>k</i>, <i>n </i>∈ <b>R</b>. In the theory of the Boltzmann equation without angular cutoff, the weighted Sobolev
space plays a fundamental role. The proof is based on pseudodifferential calculus, and, in general,
for a specific class of Weyl quantization, the <i>L</i><sup>2</sup> dissipation implies <i>H<sup>k</sup><sub>n</sub></i> dissipation. This kind of
estimate is also known as Gårding's inequality.