相关论文: Global weak solutions for a three-component Camass…
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…
In this paper we discuss integrable higher order equations {\em of Camassa-Holm (CH) type}. Our higher order CH-type equations are "geometrically integrable", that is, they describe one-parametric families of pseudo-spherical surfaces, in a…
In this paper, we consider the Cauchy problem to the Ericksen-Leslie system of liquid crystals in $\mathbb R^3$. Global well-posedness of strong solutions are obtained under the condition that the product of $\|u_0\|_2+\|\nabla d_0\|_2$ and…
We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$.
We use a sticky particle method to show global existence of (energy) conservative sticky $N$-peakon solutions to the modified Camassa-Holm equation. A dispersion regularization is provided as a selection principle for the uniqueness of…
We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position-dependent noise term. We establish the existence of weak…
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…
We consider the following Cauchy problem for weakly coupled systems of semi-linear damped elastic waves with a power source non-linearity in three-dimensions: \begin{equation*} U_{tt}-a^2\Delta U-\big(b^2-a^2\big)\nabla\text{div }…
We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time…
We study global conservative solutions of the Cauchy problem for the Camassa-Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.
We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa--Holm equation. New proofs of asymptotic behavior of the solutions are given. In particular we recover well-known collision conditions. Additionally…
We study here the existence of solitary wave solutions of a generalized two-component Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped…
In this paper we construct global weak conservative solutions of the Camassa-Holm equation on the periodic domain. We first express the equation in Lagrangian flow variable $\eta$ and then transform it using a change of variable…
In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear…
This paper is mainly concerned with the Cauchy problem for a generalized Camassa-Holm equation with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time. Then, we present…
In this paper, the system of particles coupled with fluid is considered. The particles are described by a Vlasov equation, and the fluid is governed by a forced Navier-Stokes equations. The interaction with fluid phase governed by…
The coupled quasilinear Keller-Segel-Navier-Stokes system is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\Omega\subseteq \mathbb{R}^3$ with…
We consider a 3$\times$3 spectral problem which generates four-component CH type systems. The bi-Hamiltonian structure and infinitely many conserved quantities are constructed for the associated hierarchy. Some possible reductions are also…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in…