Lagrangian-Eulerian Methods for Uniqueness in Hydrodynamic Systems
نویسنده
چکیده
We present a Lagrangian-Eulerian strategy for proving uniqueness and local existence of solutions of limited smoothness for a class of incompressible hydrodynamic models including Oldroyd-B type complex fluid models and zero magnetic resistivity magneto-hydrodynamics equations.
منابع مشابه
تحلیل دینامیکی سدهای بتنی وزنی با مدلسازی مخزن به روشهای لاگرانژی و اویلری
Because of different behavior of reservoir water and dam material, the determination of hydrodynamic pressure during earthquake is very complicated. Thus, different formulations have been presented for modeling of the dam reservoir system under dynamic loading such as earthquake. These formulations can be categorized into two general groups, which are Lagrangian and Eulerian, each having advant...
متن کاملEuler-Lagrange change of variables in conservation laws
We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...
متن کاملDynamic Fracture Analysis Using an Uncoupled Arbitrary Lagrangian Eulerian Finite Element Formulation
This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...
متن کاملSoftened Lagrangian Hydrodynamics for Cosmology
A new approach to cosmological hydrodynamics is discussed which is based on a moving, quasi-Lagrangian mesh. The softened Lagrangian hydrodynamics (SLH) method utilizes a high resolution Lagrangian hydrodynamic code combined with a low resolution Eulerian solver to deal with severe mesh distortions. Most of the volume of a simulation is treated with the Lagrangian code and only in sites where t...
متن کاملStochastic Eulerian-lagrangian Methods for Fluid-structure Interactions with Thermal Fluctuations and Shear Boundary Conditions
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal fluctuations, and externally driven shear flows. A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical system. Micros...
متن کامل