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Journal of Evolution Equations : Volume 17

Journal of Evolution Equations : Volume 17, Issue 1, March 2017

On the Stokes resolvent estimates for cylindrical domains

Cauchy problems for parabolic equations in Sobolev–Slobodeckii and Hölder spaces on uniformly regular Riemannian manifolds

Global wellposedness for a class of reaction–advection–anisotropic-diffusion systems

Strong well-posedness for a class of dynamic outflow boundary conditions for incompressible Newtonian flows

Real interpolation with weighted rearrangement invariant Banach function spaces

An integral inequality for the invariant measure of a stochastic reaction–diffusion equation

Maximal regularity for the thermoelastic plate equations with free boundary conditions

Regularity of stochastic integral equations driven by Poisson random measures

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Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type

New criteria for the $${H^\infty}$$ -calculus and the Stokes operator on bounded Lipschitz domains

Global solvability of Moore–Gibson–Thompson equation with memory arising in nonlinear acoustics

Hadamard-type formulas via the Maslov form

Linearized stability for nonlinear Volterra equations

Kernel estimates for elliptic operators with second-order discontinuous coefficients

Regularity of stochastic Volterra equations by functional calculus methods

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Well-posedness and longtime behavior for the Westervelt equation with absorbing boundary conditions of order zero

Domains of fractional powers of the heat–structure operator with viscoelastic damping: regularity and control-theoretic implications

Stability, instability, and blowup for time fractional and other nonlocal in time semilinear subdiffusion equations

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Strong well-posedness for a class of dynamic outflow boundary conditions for incompressible Newtonian flows

Content Provider	Springer Nature Link
Author	Kashiwabara, Takahito Köhne, Matthias Bothe, Dieter
Copyright Year	2016
Abstract	Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier–Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the outlet. As a key building block for the analysis of such problems, we consider the Stokes equations with such dynamic outflow boundary conditions in a halfspace and prove the existence of a strong solution in the appropriate Sobolev–Slobodeckij setting with $${L_p}$$ (in time and space) as the base space for the momentum balance. For nonvanishing stress contribution in the boundary condition, the problem is actually shown to have $${L_p}$$ -maximal regularity under the natural compatibility conditions. Aiming at an existence theory for problems in weakly singular domains, where different boundary conditions apply on different parts of the boundary such that these surfaces meet orthogonally, we also consider the prototype domain of a wedge with opening angle $${\frac{\pi}{2}}$$ and different combinations of boundary conditions: Navier-Slip with Dirichlet and Navier-Slip with the dynamic outflow boundary condition. Again, maximal regularity of the problem is obtained in the appropriate functional analytic setting and with the natural compatibility conditions.
Ending Page	171
Page Count	41
Starting Page	131
File Format	PDF
ISSN	14243199
e-ISSN	14243202
Journal	Journal of Evolution Equations
Issue Number	1
Volume Number	17
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-09-19
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Local-in-time well-posedness Navier–Stokes equations Analysis Maximal regularity Stokes and related (Oseen, etc.) flows Fourier integral operators Dynamic boundary condition Incompressible Newtonian flows Existence, uniqueness, and regularity theory Artificial boundary condition Stokes equations Navier-Stokes equations
Content Type	Text
Resource Type	Article
Subject	Mathematics

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