Related papers: On the Cauchy problem for the cutoff Boltzmann equ…

The existence of global renormalized solutions to the Boltzmann equation with long-range interactions without angular cutoff was first established by Alexandre and Villani [Comm. Pure Appl. Math., 55(1), 30-70, 2002]. Their result relies on…

This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility…

The study of positivity of solutions to the Boltzmann equation goes back to Carleman (1933), and the initial argument of Carleman was developed byPulvirenti-Wennberg (1997), the second author and Briant (2015). The appearance of a lower…

This work is concerned with the generation of decay estimates in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff on a bounded spatial domain for hard and moderately soft potentials. We work…

In this paper, we investigate the existence of a global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum. Precisely, when the far-field density is vacuum…

In the present work, we investigate estimates of regularity for weak solutions to the non-cutoff Boltzmann equation with soft potentials. We restrict our focus to the so-called "typically rough and slowly decaying data", which is…

We consider the Cauchy problem to the 3D fractional Schr\"odinger equation with quadratic interaction of $u\bar u$ type. We prove the global existence of solutions and scattering properties for small initial data. For the proof, one novelty…

This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with $-3<\gamma<-2s$ and $1/2\leq s<1$, where…

In this paper, the finite time blow-up of smooth solutions to the Cauchy problem for full Euler-Poisson equations and isentropic Euler-Poisson equations with repulsive forces or attractive forces in high dimensions $(n\geq3)$ is proved for…

In this work, we prove the existence, uniqueness and smoothing properties of the solution to the Cauchy problem for the spatially homogeneous Boltzmann equation with Debye-Yukawa potential for probability measure initial datum.

We construct a unique global solution to the Cauchy problem of the 3D Boltzmann equation for initial data around the Maxwellian in the spatially critical homogeneous Besov space…

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of…

The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter $\e$ tends to…

We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform…

The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…

We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=\mu+\mu^{\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the…

We study the Cauchy problem for the relativistic Boltzmann equation near relativistic Maxwellians in the whole space. The purpose of this article is to handle hard potentials, and for initial data with finite $L^\infty$ norm, to construct…

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 $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions…

For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far…

In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in $\R^3$. By making use of Bourgain's method in conjunction with a precise Strichartz estimate of S.Klainerman and D.Tataru, we…