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 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 establish the maximal hyperbolic development of Cauchy data for the multi-dimensional
compressible Euler equations. For an open set of compressive and generic $ H^ 7$ initial …

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 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 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 …

We examine the two-dimensional Euler equations including the local energy (in) equality as
a differential inclusion and show that the associated relaxation essentially reduces to the …

We prove via convex integration a result that allows to pass from a so-called subsolution of
the isentropic Euler equations (in space dimension at least 2) to exact weak solutions. The …

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 …