6 papers
Sharp non-uniqueness of weak solutions to the semilinear wave equation
Peng Qu, Mingxin Zhang
In this paper, we establish a sharp non-uniqueness result to the semilinear wave equation \[ \partial_{tt}u-\partial_{xx} u= Θ_1(\partial_t u)^2 + Θ_2(\partial_x u)^2. \] For any $…
Sharp non-uniqueness for the hyper-viscous compressible 3D Oldroyd-type models: Beyond the Lions exponent
Haobin Li, Peng Qu, Zirong Zeng +1
We prove the non-uniqueness of weak solutions to the three-dimensional hyper-viscous compressible Oldroyd-type model with general pressure laws and Newtonian viscous. Using an inte…
Non-uniqueness for the hypo-dissipative compressible 3D magnetohydrodynamic equations
Haobin Li, Peng Qu
We consider the compressible 3D magnetohydrodynamic (MHD) equations under general pressure laws. For all hypo-viscosities and hypo-resistivity with $α_1,α…
Non-uniqueness of weak solutions to the 3-D stationary MHD equations in Besov space with negative regularity index
Peng Qu, Mingxin Zhang
In this paper, we study the 3-D incompressible fractional stationary MHD equations on the torus . For fractional power indices we prove that there exist…
Non-uniqueness for the nonlinear dynamical Lamé system
Shunkai Mao, Peng Qu
We consider the Cauchy problem for the nonlinear dynamical Lamé system with double wave speeds in a -dimensional periodic domain. Moreover, the equations can be transf…
The null condition in elastodynamics leads to non-uniqueness
Shunkai Mao, Peng Qu
We consider the Cauchy problem for the system of elastodynamic equations in two dimensions. Specifically, we focus on materials characterized by a null condition imposed on the qua…