Well-Posedness of the Iterative Boltzmann Inversion

Simultaneous Iterative Boltzmann Inversion for Coarse-Graining of Polyurea

Polyurea is an alternating copolymer with excellent viscoelastic properties for dissipating shock and impact loads; however, a molecular-level understanding of how its chemistry relates to its performance remains elusive. While molecular dynamics simulations can in theory draw connections between molecular structure and viscoelastic properties, in practice the long relaxation times associated w...

On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity

Abstract. We prove an inequality on the Kantorovich-Rubinstein distance – which can be seen as a particular case of a Wasserstein metric– between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, but with a moderate angular singularity. Our method is in the spirit of [7]. We deduce some well-posedness and stability results in the physically relevant cases of ...

Well-posedness of Hybrid Systems

Well-posedness of the Water-waves Equations

1.1. Presentation of the problem. The water-waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect, incompressible, irrotational fluid under the influence of gravity. In this paper, we restrict our attention to the case when the surface is a graph parameterized by a function ζ(t,X), where t denotes th...

Well-posedness of the Ericksen-leslie System

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the GinzburgLandau approximation, we construct an approximate system with the dissipated energy based on a new formulation of th...