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pro vyhledávání: '"Holmer, Justin"'
Autor:
Chen, Xuwen, Holmer, Justin
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, effectively, the inverse power law model, from the many-body dynamics as
Externí odkaz:
http://arxiv.org/abs/2312.08239
Autor:
Chen, Xuwen, Holmer, Justin
Publikováno v:
Annals of PDE 10 (2024), no. 2, Paper No. 14, 1-44
We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium n
Externí odkaz:
http://arxiv.org/abs/2206.11931
The Benjamin Ono equation with a slowly varying potential is $$ \text{(pBO)} \qquad u_t + (Hu_x-Vu + \tfrac12 u^2)_x=0 $$ with $V(x)=W(hx)$, $0< h \ll 1$, and $W\in C_c^\infty(\mathbb{R})$, and $H$ denotes the Hilbert transform. The soliton profile i
Externí odkaz:
http://arxiv.org/abs/2106.02971
Autor:
Chen, Xuwen, Holmer, Justin
Publikováno v:
Annals of PDE Vol. 8 (2022), Article 11, 1-39
We consider the derivation of the defocusing cubic nonlinear Schr\"{o}dinger equation (NLS) on $\mathbb{R}^{3}$ from quantum $N$-body dynamics. We reformat the hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering theorem for t
Externí odkaz:
http://arxiv.org/abs/2104.06086
Autor:
Chen, Xuwen, Holmer, Justin
Publikováno v:
Forum of Mathematics, Pi Vol. 10 (2022), e3 1-49
We consider the $\mathbb{T}^{4}$ cubic NLS which is energy-critical. We study the unconditional uniqueness of solution to the NLS via the cubic Gross-Pitaevskii hierarchy, an uncommon method, and does not require the existence of solution in Strichar
Externí odkaz:
http://arxiv.org/abs/2006.05915
We consider the quadratic Zakharov-Kuznetsov equation $$ \partial_t u + \partial_x \Delta u + \partial_x u^2 =0 $$ on $\mathbb{R}^3$. A solitary wave solution is given by $Q(x-t,y,z)$, where $Q$ is the ground state solution to $-Q + \Delta Q + Q^2 =0
Externí odkaz:
http://arxiv.org/abs/2006.00193
Akademický článek
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We consider the 1D nonlinear Schr\"odinger equation with focusing point nonlinearity. "Point" means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta function supported at the origin. This equation is used
Externí odkaz:
http://arxiv.org/abs/1904.09066
Autor:
Kwak, Kyoung Hyun, He, Yu, Kim, Youngki, Fan, Shihong, Kim, Heeseong, Holmer, Justin, Chen, Yue Ming, Link, Brian
Publikováno v:
In IFAC PapersOnLine 2023 56(3):139-144
We prove that near-threshold negative energy solutions to the 2D cubic ($L^2$-critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof consists of several steps. First, we show that if the blow-up conclusion i
Externí odkaz:
http://arxiv.org/abs/1810.05121