Well/ill-posedness of the Boltzmann equation with soft potential

DOI10.1007/s00220-024-05157-6MaRDI QIDQ6640611

Zhifei Zhang, Shunlin Shen, Xuwen Chen

Publication date: 20 November 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Qxx) Qualitative properties of solutions to partial differential equations (35Bxx) General topics in partial differential equations (35Axx)

Cites Work

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• Global well-posedness in spatially critical Besov space for the Boltzmann equation
• The Gross-Pitaevskii hierarchy on general rectangular tori
• Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation
• On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
• Collapsing estimates and the rigorous derivation of the 2d cubic nonlinear Schrödinger equation with anisotropic switchable quadratic traps
• Global well-posedness of the Boltzmann equation with large amplitude initial data
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• On the global existence of mild solutions to the Boltzmann equation for small data in \(L^D\)
• A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on \(\mathbb{T}^3\) from the dynamics of many-body quantum systems
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Hydrodynamic limits of the Boltzmann equation
• Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform
• Self-spreading and strength of singularities for solutions to semilinear wave equations
• Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian
• Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension
• The Boltzmann equation and its applications
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The mathematical theory of dilute gases
• Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• Entropy dissipation and long-range interactions
• Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces
• On the ill-posedness of some canonical dispersive equations.
• Convolution inequalities for the Boltzmann collision operator
• Moments and regularity for a Boltzmann equation via Wigner transform
• Quantitative derivation and scattering of the 3D cubic NLS in the energy space
• The unconditional uniqueness for the energy-supercritical NLS
• The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics
• Well-posedness and scattering for the Boltzmann equations: soft potential with cut-off
• Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform
• Local existence with mild regularity for the Boltzmann equation
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
• The Boltzmann equation, Besov spaces, and optimal time decay rates in \(\mathbb{R}_x^n\)
• Exponential decay for soft potentials near Maxwellian
• On the rigorous derivation of the 3D cubic nonlinear Schrödinger equation with a quadratic trap
• Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates
• On the Cauchy problem for the cutoff Boltzmann equation with small initial data
• Global well-posedness of a binary-ternary Boltzmann equation
• ON NONNEGATIVITY OF SOLUTIONS OF THE BOLTZMANN EQUATION
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti
• Global classical solutions of the Boltzmann equation without angular cut-off
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• Endpoint Strichartz estimates
• Space‐time estimates for null forms and the local existence theorem
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Correlation Structures, Many-Body Scattering Processes, and the Derivation of the Gross–Pitaevskii Hierarchy
• A bilinear estimate with applications to the KdV equation
• Quadratic forms for the 1-D semilinear Schrödinger equation
• Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
• Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on
• Unconditional uniqueness results for the nonlinear Schrödinger equation
• Exact smoothing properties of Schrodinger semigroups
• Local well-posedness for quasi-linear problems: A primer
• The derivation of the compressible Euler equation from quantum many-body dynamics
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel

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