相关论文: The Boltzmann equation in the homogeneous critical…
Departing from the weak solution, we prove the uniqueness, smoothing estimates and the global dynamics for the non cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. Our results show that the behavior of the…
The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$ approach, we prove the global…
In this paper, we prove that if the initial data $\theta_0$ and its Riesz transforms ($\mathcal{R}_1(\theta_0)$ and $\mathcal{R}_2(\theta_0)$) belong to the space $(\overline{S(\mathbb{R}^2))}^{B_{\infty}^{1-2\alpha ,\infty}}$, where…
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
We consider the Cauchy problem for the inhomogeneous biharmonic nonlinear Schr\"{o}dinger (IBNLS) equation \[iu_{t} +\Delta^{2} u=\lambda |x|^{-b}|u|^{\sigma}u,\;u(0)=u_{0} \in H^{s} (\mathbb R^{d}),\] where $\lambda\in \mathbb R$, $d\in…
We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density \r{ho}(x) on an infinite graph which supports the Sobolev inequality. For nonnegative solutions when p > 2, we prove the precise rate of…
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…
In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three space dimensions. The results are based on the…
We give a new decay framework for general dissipative hyperbolic system and hyperbolic-parabolic composite system, which allow us to pay less attention on the traditional spectral analysis in comparison with previous efforts. New…
The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann…
We study the well-posedness of the Cauchy problem with Dirichlet or Neumann boundary conditions associated to an H 1 -critical semilinear wave equation on a smooth bounded 2D domain {\Omega}. First, we prove an appropriate Strichartz type…
We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space H^{s_1,s_2}(R^2) with s_1 > -1/2 and s_2 \geq 0. On the H^{s_1,0}(R^2) scale this…
This is the first one of two papers on the global dynamics of the original Boltzmann equations without angular cutoff on the torus. We address the problem for the hard potentials and Maxwellian molecules in the present paper. The case of…
We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous non-cutoff Boltzmann equation with Maxwellian molecules enjoys the same Gelfand-Shilov regularizing effect as the Cauchy problem defined by the…
Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly…
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…
We consider the Cauchy problem for the generalized Zakharov-Kuznetsov-Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative equations, which has a spatial anisotropic dissipative term $-\mu u_{xx}$. In this paper, we…
The present paper deals with the Cauchy problem of a compressible generic two-fluid model with capillarity effects in any dimension $N\geq2$. We first study the unique global solvability of the model in spaces with critical regularity…
We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…