Related papers: Global Existence Proof for Relativistic Boltzmann …
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is…
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…
In this work, we investigate the existence and uniqueness of solutions to the following 2D and 3D convective Brinkman-Forchheimer extended Darcy equations defined on a bounded smooth domain $\Omega\subset\mathbb{R}^d$, $d\in\{2,3\}$,…
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…
Motivated by Duan et al.[Global Mild Solutions of the Landau and Non-Cutoff Boltzmann Equations, Comm. Pure Appl. Math., 74(5), 932-1020.], the global existence of mild solutions to the Vlasov-Maxwell-Fokker-Planck system near a global…
This paper is concerned with the hypercoercivity property of solutions to the Cauchy problem on the linear Boltzmann equation with a confining potential force. We obtain the exponential time rate of solutions converging to the steady state…
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a…
We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity:…
We prove global existence and modified scattering for the solutions of the Cauchy problem to the fractional Korteweg-de Vries equation with cubic nonlinearity for small, smooth and localized initial data.
In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smooth, time-dependent, elliptic part having a variational…
The Lagrange-d'Alembert equations with constraints belonging to $H^{1,\infty}$ have been considered. A concept of weak solutions to these equations has been built. Global existence theorem for Cauchy problem has been obtained.
This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D…
We prove a global well-posedness result for the 2D Muskat problem with surface tension. Given any regular enough initial data which is small in some critical space but possibly large in Lipschitz, we prove that the associated Cauchy problem…
We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…
We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is…
We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and…
In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for…
We consider the Neumann and Cauchy problems for positivity preserving reaction-diffusion systems of $m$ equations enjoying the mass and entropy dissipation properties. We show global classical existence in any space dimension, under the…
In this paper, we study the global well-posedness of the Boltzmann equation within the $L_{v}^{p}L_{x}^{\infty}$ framework for soft potential models with angular cutoff in a periodic box $\mathbb{T}^3$. By using a time-involved weight…