The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Dexing Feng - One of the best experts on this subject based on the ideXlab platform.

Zhaoqiang Ge - One of the best experts on this subject based on the ideXlab platform.

Toshiaki Hishida - One of the best experts on this subject based on the ideXlab platform.

  • Decay Estimates of Gradient of a Generalized Oseen Evolution Operator Arising from Time-Dependent Rigid Motions in Exterior Domains
    Archive for Rational Mechanics and Analysis, 2020
    Co-Authors: Toshiaki Hishida
    Abstract:

    Let us consider the motion of a viscous incompressible fluid past a rotating rigid body in three dimensions, where the translational and angular velocities of the body are prescribed but time-dependent. In a reference frame attached to the body, we have the Navier–Stokes system with the drift and (one half of the) Coriolis terms in a fixed exterior domain. The existence of the Evolution Operator T ( t ,  s ) in the space $$L^q$$ L q generated by the linearized non-autonomous system was proved by Hansel and Rhandi (J Reine Angew Math 694:1–26, 2014) and the large time behavior of T ( t ,  s ) f in $$L^r$$ L r for $$(t-s)\rightarrow \infty $$ ( t - s ) → ∞ was then developed by Hishida (Math Ann 372:915–949, 2018) when f is taken from $$L^q$$ L q with $$q\leqq r$$ q ≦ r . The contribution of the present paper concerns such $$L^q$$ L q - $$L^r$$ L r decay estimates of $$\nabla T(t,s)$$ ∇ T ( t , s ) with optimal rates, which must be useful for the study of stability/attainability of the Navier–Stokes flow in several physically relevant situations. Our main theorem completely recovers the $$L^q$$ L q - $$L^r$$ L r estimates for the autonomous case (Stokes and Oseen semigroups, those semigroups with rotating effect) in three dimensional exterior domains, which were established by Hishida and Shibata (Arch Ration Mech Anal 193:339–421, 2009), Iwashita (Math Ann 285, 265–288, 1989), Kobayashi and Shibata (Math Ann 310:1–45, 1998), Maremonti and Solonnikov (Ann Sc Norm Super Pisa 24:395–449, 1997) and Shibata (in: Amann, Arendt, Hieber, Neubrander, Nicaise, von Below (eds) Functional analysis and Evolution equations, the Günter Lumer volume. Birkhäuser, Basel, pp 595–611, 2008).

  • decay estimates of gradient of a generalized oseen Evolution Operator arising from time dependent rigid motions in exterior domains
    arXiv: Analysis of PDEs, 2019
    Co-Authors: Toshiaki Hishida
    Abstract:

    Let us consider the motion of a viscous incompressible fluid past a rotating rigid body in 3D, where the translational and angular velocities of the body are prescribed but time-dependent. In a reference frame attached to the body, we have the Navier-Stokes system with the drift and (one half of the) Coriolis terms in a fixed exterior domain. The existence of the Evolution Operator $T(t,s)$ in the space $L^q$ generated by the linearized non-autonomous system was proved by Hansel and Rhandi [26] and the large time behavior of $T(t,s)f$ in $L^r$ for $(t-s)\to\infty$ was then developed by the present author [33] when $f$ is taken from $L^q$ with $q\leq r$. The contribution of the present paper concerns such $L^q$-$L^r$ decay estimates of $\nabla T(t,s)$ with optimal rates, which must be useful for the study of stability/attainability of the Navier-Stokes flow in several physically relevant situations. Our main theorem completely recovers the $L^q$-$L^r$ estimates for the autonomous case (Stokes and Oseen semigroups, those semigroups with rotating effect) in 3D exterior domains, which were established by [37], [42], [39], [36] and [44].

  • large time behavior of a generalized oseen Evolution Operator with applications to the navier stokes flow past a rotating obstacle
    Mathematische Annalen, 2018
    Co-Authors: Toshiaki Hishida
    Abstract:

    Consider the motion of a viscous incompressible fluid in a 3D exterior domain D when a rigid body \(\mathbb R^3{\setminus } D\) moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, \(L^q\)-\(L^r\) smoothing action near \(t=s\) as well as generation of the Evolution Operator \(\{T(t,s)\}_{t\ge s\ge 0}\) was shown by Hansel and Rhandi (J Reine Angew Math 694:1–26, 2014) under reasonable conditions. In this paper we develop the \(L^q\)-\(L^r\) decay estimates of the Evolution Operator T(t, s) as \((t-s)\rightarrow \infty \) and then apply them to the Navier–Stokes initial value problem.

  • large time behavior of a generalized oseen Evolution Operator with applications to the navier stokes flow past a rotating obstacle
    arXiv: Analysis of PDEs, 2017
    Co-Authors: Toshiaki Hishida
    Abstract:

    Consider the motion of a viscous incompressible fluid in a 3D exterior domain when a rigid body moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, $L^q$-$L^r$ smoothing action near the initial time as well as generation of the Evolution Operator was shown by Hansel and Rhandi (J. Reine Angew. Math. 2014) under reasonable conditions. In this paper we develop the $L^q$-$L^r$ decay estimates of the Evolution Operator and then apply them to the Navier-Stokes initial value problem.

Daniel Jean Baye - One of the best experts on this subject based on the ideXlab platform.

  • sixth order factorization of the Evolution Operator for time dependent potentials
    Physical Review E, 2004
    Co-Authors: Gerald Goldstein, Daniel Jean Baye
    Abstract:

    : The Evolution Operator of a quantum system in a time-dependent potential is factorized in unitary exponential Operators at order 6. This expression is derived with the time-ordering method. It is compared with lower-order factorizations on several simple one-dimensional examples. Better accuracies are reached at sixth order for a given time step than at lower orders. Due to a significant increase of computation duration per time step, the sixth-order approximation is mainly useful when high accuracies are required.

  • fourth order factorization of the Evolution Operator for time dependent potentials
    Physics Letters A, 2003
    Co-Authors: Daniel Jean Baye, Gerald Goldstein, Pierre Capel
    Abstract:

    Abstract A unitary factorization of the Evolution Operator at order four is derived from the Magnus expansion with a time-dependent potential. Its efficiency is tested on various mesh treatments of a forced harmonic oscillator. With respect to second order, accuracies are improved by more than an order of magnitude.

Kazuyuki Fujii - One of the best experts on this subject based on the ideXlab platform.