In variational phase-field modeling of brittle fracture, the functional to be minimized is not
convex, so that the necessary stationarity conditions of the functional may admit multiple …

We give a survey of recent results on weak-strong uniqueness for compressible and
incompressible Euler and Navier-Stokes equations, and also make some new observations …

The butterfly effect is today commonly identified with the sensitive dependence of
deterministic chaotic systems upon initial conditions. However, this is only one facet of the …

Stressed dislocation pattern formation in crystal plasticity at finite deformation is
demonstrated for the first time. Size effects are also demonstrated within the same …

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance)
laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or …

The book focuses on stability and approximation results concerning recent numerical
methods for the numerical solution of hyperbolic conservation laws. The work begins with a …

We prove a version of Onsager's conjecture on the conservation of energy for the
incompressible Euler equations in the context of statistical solutions, as introduced recently …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

Statistical solutions are time-parameterized probability measures on spaces of integrable
functions, which have been proposed recently as a framework for global solutions and …

We propose and study the framework of dissipative statistical solutions for the
incompressible Euler equations. Statistical solutions are time-parameterized probability …