7月 25（金） 13:30～

発表者

Massimo Tessarotto (所属：University of Trieste, Italy)

題目

Inverse kinetic approaches for classical and quantum fluids

概要

 
In fluid dynamics the state of the fluid, represented by an appropriate
set of suitably smooth real tensor fields, the so-called fluid fields,
is advanced in time by means of a complete set of pde's (the fluid
equations), sub ject to suitable initial and boundary conditions. In
particular, in the framework of the axiomatic approach to continuum
mechanics, fluid dynamics is usually formulated by requiring that the
state of the fluid is by assumption defined everywhere in the whole
space-time, or in an appropriate open subset, denoted as existence
domain. Hence, this means that in this domain the fluid fields must
necessarily be identified with strong solutions of the fluid equations.
The problem of the explicit construction of strong solutions of the
fluid equations, as well the very global existence and regularity of the
same solutions in unbounded domains, remains at the date a formidable
and still largely unsolved, theoretical problem. In fact, generally the
fluid equations represent a mixture of hyperbolic and elliptic pdes,
which are extremely hard to study both analytically and numerically.
This has motivated in the past efforts to replace the fluid equations
with other equations, possibly simpler to solve or mathematically more
elegant. This includes the possibility, well known in the literature, to
recur to phase-space formulations, based for example on the microscopic
nature of the (real) fluids. In this connection a particular viewpoint -
which applies in principle both to classical and quantum fluids - is
represented by the class of so-called inverse problems, involving the
search of a so-called inverse kinetic theory (IKT) able to yield the
complete set of fluid equations for the fluid fields, via a suitable
correspondence principle whereby the same equations are identified with
appropriate moment equations constructed in terms of the relevant
kinetic equation. Among the infinite possible IKT's, special relevance
pertains to those in which the kinetic equation which advances in time
the kinetic distribution function generates a suitable classical
dynamical system and applies specifical ly to strong solutions of the
fluid equations. As a consequence the time evolution of the fluid fields
results uniquely determined by the same dynamical system. In addition,
due to the intrinsic freedom in the choice of the IKT, it is possible to
impose further important requirements, such as: 1) that the IKT applies
to arbitrary (but suitably defined) initial and boundary conditions for
the fluid fields; 2) that the IKT is non-asymptotic, i.e., it does not
depend on any infinitesimal parameter; 3) that the IKT is complete,
i.e., it provides the complete set of fluid equations and all the fluid
fields are uniquely defined in terms of suitably- prescribed moments of
the kinetic distribution function; 4) that the IKT is self-consistent,
i.e., the fluid fields are determined uniquely independently of the
initial data to be placed on the kinetic distribution function.
In this presentation basic features and consequences following from
IKT's of this type, and holding both for classical and quantum fluids,
will be analyzed.
      

場所

京都大学 基礎物理学研究所 湯川記念館・大会議室Y306

地図 (Map)