P. Tolksdorf

activity

20172022

most citedStrong Time Periodic Solutions to the Bidomain Equations with FitzHugh-Nagumo Type Nonlinearities

2 citations · 2 across the 6 of their papers we have counts for

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math.AP2022

Critical regularity issues for the compressible Navier--Stokes system in bounded domains

Raphaël Danchin, Patrick Tolksdorf

We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $R^{d}$ (with $d \geq 2$ ). In a critical regularity setting, we establish local w…

math.AP2021

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

Patrick Tolksdorf

We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on $L_{σ}^{2} (R^{d})$ . Such estimates are well-kn…

math.AP2020

A non-local approach to the generalized Stokes operator with bounded measurable coefficients

Patrick Tolksdorf

We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L_{σ}^{p} (R^{d})$ , $d \geq 2$ , for $\lvert 1 / p - 1 / 2 \rvert < 1…

math.AP2020

Lorentz spaces in action on pressureless systems arising from models of collective behavior

Raphaël Danchin, Piotr Boguslaw Mucha, Patrick Tolksdorf

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 be…

math.AP2019

The Stokes resolvent problem: Optimal pressure estimates and remarks on resolvent estimates in convex domains

Patrick Tolksdorf

The Stokes resolvent problem $λ u - Δ u + \nabla ϕ = f$ with $div (u) = 0$ subject to homogeneous Dirichlet or homogeneous Neumann-type boundary conditions is investigated. In…

math.AP2019

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory

Patrick Tolksdorf, Keiichi Watanabe

We show that the Stokes operator defined on $L_{σ}^{p} (Ω)$ for an exterior Lipschitz domain $Ω \subset R^{n}$ $(n \geq 3)$ admits maximal regularity provided that $p$ s…

Critical regularity issues for the compressible Navier--Stokes system in bounded domains

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

A non-local approach to the generalized Stokes operator with bounded measurable coefficients

Lorentz spaces in action on pressureless systems arising from models of collective behavior

The Stokes resolvent problem: Optimal pressure estimates and remarks on resolvent estimates in convex domains

The Navier--Stokes equations in exterior Lipschitz domains: Lp-theory

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory