Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Tolksdorf, Patrick"'
Autor:
Haardt, Luca, Tolksdorf, Patrick
We establish the Kato square root property for the generalized Stokes operator on $\mathbb{R}^d$ with bounded measurable coefficients. More precisely, we identify the domain of the square root of $Au := - \operatorname{div}(\mu \nabla u) + \nabla \ph
Externí odkaz:
http://arxiv.org/abs/2410.18787
Autor:
Gabel, Fabian, Tolksdorf, Patrick
Publikováno v:
Journal of Differential Equations 340 (2022) 227-272
We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. We prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying the condition $\lvert 1 / p - 1 / 2 \
Externí odkaz:
http://arxiv.org/abs/2204.05867
Autor:
Danchin, Raphaël, Tolksdorf, Patrick
We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $\mathbb{R}^d$ (with $d\geq2$). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global well-posedness
Externí odkaz:
http://arxiv.org/abs/2201.03823
Autor:
Tolksdorf, Patrick
We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on $\mathrm{L}^2_{\sigma} (\mathbb{R}^d)$. Such estimates are well-known for elliptic equations in the form of pointwise heat kernel
Externí odkaz:
http://arxiv.org/abs/2103.03226
Autor:
Tolksdorf, Patrick
We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L^p_{\sigma} (\mathbb{R}^d)$, $d \geq 2$, for $\lvert 1 / p - 1 / 2 \rvert < 1 / d$. These include optimal resolvent bounds and the property o
Externí odkaz:
http://arxiv.org/abs/2011.13771
An $\mathrm{L}_1$-maximal regularity theory for parabolic evolution equations inspired by the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, the approach yields a framework allowing global-in-time control of the c
Externí odkaz:
http://arxiv.org/abs/2011.07918
We are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only
Externí odkaz:
http://arxiv.org/abs/2005.05603
Autor:
Tolksdorf, Patrick
The aim of this article is to deepen the understanding of the derivation of $\mathrm{L}^p$-estimates of non-local operators. We review the $\mathrm{L}^p$-extrapolation theorem of Shen which builds on a real variable argument of Caffarelli and Peral a
Externí odkaz:
http://arxiv.org/abs/2004.11174
Autor:
Tolksdorf, Patrick
The Stokes resolvent problem $\lambda u - \Delta u + \nabla \phi = f$ with $\mathrm{div}(u) = 0$ subject to homogeneous Dirichlet or homogeneous Neumann-type boundary conditions is investigated. In the first part of the paper we show that for Neumann
Externí odkaz:
http://arxiv.org/abs/1911.06231
Let $\Omega \subseteq \mathbb{R}^d$ be open and $D\subseteq \partial\Omega$ be a closed part of its boundary. Under very mild assumptions on $\Omega$, we construct a bounded Sobolev extension operator for the Sobolev space $\mathrm{W}^{k , p}_D (\Ome
Externí odkaz:
http://arxiv.org/abs/1910.06009