We construct a fundamental piece of the boundary of the maximal globally hyperbolic
development (MGHD) of Cauchy data for the multi-dimensional compressible Euler …

We prove the non-uniqueness of weak solutions to 3D hyper viscous and resistive MHD in
the class L t γ W xs, p, where the viscosity and resistivity can be larger than the Lions …

We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD for
short) equations. The constructed weak solutions do not conserve the magnetic helicity and …

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-
dimensional periodic domain under general pressure laws. For any smooth initial density …

Fluids can behave in a highly irregular, turbulent way. It has long been realised that,
therefore, some weak notion of solution is required when studying the fundamental partial …

We prove the non-uniqueness of weak solutions to 3D hyper viscous and resistive MHD in
the class $ L^\gamma_tW^{s, p} _x $, where the exponents $(s,\gamma, p) $ lie in two …

We construct a fundamental piece of the boundary of the maximal globally hyperbolic
development (MGHD) of Cauchy data for the multi-dimensional compressible Euler …

We consider the Cauchy problem for the isentropic compressible Euler–Maxwell equations
under general pressure laws in a three-dimensional periodic domain. For any smooth initial …

We adapt Glimm's approximation method to the framework of convex integration to show
density of wild data for the (complete) Euler system of gas dynamics. The desired infinite …

Contrary to the incompressible case, not every measure-valued solution of the compressible
Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In …