Related papers: The existence and uniqueness of global admissible …
In this paper, we study the global conservative weak solutions for a class of nonlinear dispersive wave equations after wave breaking. We first transform the equations into an equivalent semi-linear system by introducing new variables. We…
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…
This paper is concerned with the existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation on real line. By introducing some new variables, the equation is transformed into two different semi-linear systems.…
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…
In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent…
In this paper,for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get…
We study in this article a variation of the Whitham equation which was introduced as an alternative to the KdV equation. We first prove the global existence of weak solutions, then we establish a regularity criterion from which we deduce…
In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations…
We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…
In this paper, we prove the uniqueness of energy conservative Holder continuous weak solution to a general quasilinear wave equation by the analysis of characteristics. This result has no restriction on the size of solutions, i.e. it is a…
In this paper, we mainly consider about the existence and uniqueness of global weak solutions for the two-component Novikov system. We first recall some results and definitions of strong solutions and weak solutions for the system, then by…
We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$ with…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
We establish a weak-strong uniqueness result for the isentropic compressible Euler equations, that is: As long as a sufficiently regular solution exists, all energy-admissible weak solutions with the same initial data coincide with it. The…
This paper studies the properties of weak solutions to a class of space-time fractional parabolic-elliptic Keller-Segel equations with logistic source terms in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of weak…
We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…
In this paper we mainly investigate the Cauchy problem of a generalized Camassa-Holm equation. First by this relationship between the Degasperis-Procesi equation and the generalized Camassa-Holm equation, we then obtain two global…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…
We prove that dissipative weak solutions of the Camassa-Holm equation are unique. Thus we complete the global well-posedness theory of this celebrated model of shallow water, initiated by a general proof of existence in [Z. Xin, P. Zhang…