Related papers: Global weak solutions for a periodic two-component…
A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…
We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp…
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…
This paper is concerned with blow-up phenomena and global existence for the periodic two-component Dullin-Gottwald-Holm system. We first obtain several blow-up results and the blow-up rate of strong solutions to the system. We then present…
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…
We propose a new two-component geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the two-component Hunter-Saxton…
In this paper we consider the existence of global weak entropy solutions for a particualr nonsymmetric Keyfitz-Kranzer type system, by using the compensated compactness method we get bounde entropy weak solutions
We consider the Cauchy problem for the electron magnetohydrodynamics model in the supercritical regime. For rough initial data in $\mathcal H^{-s}(\mathbb T^n)$ with $s>0$, we obtain global in time weak solutions almost surely via an…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
In this paper, we study the bilinear form and the general N-soliton solution for a two-component Hunter-Saxton (2-HS) equation, which is the short wave limit of a twocomponent Camassa-Holm equation. By defining a hodograph transformation…
In this paper, we prove that the existence and uniqueness of globally weak solutions to the Cauchy problem for the weakly dissipative Camassa-Holm equation in time weighted $H^1$ space. First, we derive an equivalent semi-linear system by…
We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…
Considered herein is a multi-component Novikov equation, which admits bi-Hamiltonian structure, infinitely many conserved quantities and peaked solutions. In this paper, we deduce two blow-up criteria for this system and global existence…
In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which…
The present work is mainly concerned with global existence for the two-component Camassa-Holm system and the modified two-component Camassa-Holm system. By discovering new conservative quantities of these systems, we prove several new…
We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of…
We establish the concept of $\alpha$-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either $\alpha(x)=1$ or $0\leq \alpha(x)<1$ for all $x\in \mathbb{R}$. Furthermore, we investigate the Lipschitz…
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an…
This paper deals with the existence, multiplicity, minimal complexity and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V.…