相关论文: Global weak solutions for a three-component Camass…
We show that the Cauchy problem for the Camassa-Holm equation has a unique, global, weak, and dissipative solution for any initial data $u_0\in H^1(\mathbb{R})$, such that $u_{0,x}$ is bounded from above almost everywhere. In particular, we…
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…
In this paper, we study an integrable system with both quadratic and cubic nonlinearity: $m_t=bu_x+1/2k_1[m(u^2-u^2_x)]_x+1/2k_2(2m u_x+m_xu)$, $m=u-u_{xx}$, where $b$, $k_1$ and $k_2$ are arbitrary constants. This model is kind of a cubic…
This work is devoted to the global existence of weak solution for a general isothermal model of capillary fluids derived by C. Rohde, which can be used as a phase transition model. This article is structured in the following way: first of…
We consider an initial-boundary value problem for the incompressible four-component Keller-Segel-Navier-Stokes system with rotational flux $$\left\{\begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c)-nm,\quad x\in…
We derive the global existence of weak solutions of the Shigesada-Kawasaki-Teramoto systems in space dimension less or equal to 4 with a rather general condition on the coefficients. The existence is established using finite differences in…
In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, using Banach fixed point theorem, we establish the local well-posedness of…
The Cauchy problem for semi-linear Klein-Gordon equations is considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. The local and global well-posedness of the Cauchy problem is considered in Sobolev spaces. The non-existence of…
In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D…
This paper considers the Cauchy problem for the quasilinear hyperbolic system of balance laws in $\mathbb{R}^d$, $d\ge 2$. The system is partially dissipative in the sense that there is an eigen-family violating the Kawashima condition. By…
We show that wave breaking occurs for the modified Camassa-Holm (mCH) equation. Next we classify all traveling wave solutions of the modified Camassa-Holm equation in the weak sense via parametrization of their maxima, minima and wave…
A spectral and the inverse spectral problem are studied for the two-component modified Camassa-Holm type for measures associated to interlacing peaks. It is shown that the spectral problem is equivalent to an inhomogenous string problem…
In this paper, we study the Cauchy problem of a periodic 2-component $\mu$-Hunter-Saxton system. We first establish the local well-posedness for the periodic 2-component $\mu$-Hunter-Saxton system by Kato's semigroup theory. Then, we derive…
In this paper, we investigate the orbital stability problem of peakons for a modified Camassa-Holm equation with both quadratic and cubic nonlinearity. This equation was derived from integrable theory and admits peaked soliton (peakon) and…
The aim of the note is to discuss different definitions of solutions to the Cauchy problem for the Navier-Stokes equations with the initial data belonging to the Lebesgue space $L_3(\mathbb R^3)$
This paper studies the three-dimensional stochastic chemotaxis-Navier-Stokes (SCNS) system subjected to a L\'{e}vy-type random external force in bounded domain. Up to now, the existing results concerning global solvability of SCNS system…
In this paper, we show that the peakon (peaked soliton) solutions can be recovered from the smooth soliton solutions, in the sense that there exists a sequence of smooth N-soliton solutions of the dispersion Camassa-Holm equation converging…
The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is…
We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of…
We introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $\dot{B}^{-1+\frac{3}{p}}_{p,\infty}$, $p > 3$. These solutions satisfy a certain…