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Karoline Disser

Publications and source records attributed to Karoline Disser.

10 recordsLinked to original sources
arXiv2025

Strong stability and the Schiffer Conjecture for the fluid-elastic semigroup

In a series of papers, Avalos and Triggiani established the fluid-elastic semigroup for the coupled Stokes-Lam\'e system modelling the coupled dynamics of a linearly elastic structure immersed in a viscous Newtonian fluid. They analyzed the spectrum of its generator and proved that the semigroup is strongly stable, if the domain of the structure satisfies a geometric condition, i.e. it is not a bad domain. We extend these results in two directions: first, for bad domains, we prove a decomposition of the dynamics into a strongly stable part and a pressure wave, a special solution of the Dirichlet-Lam\'e system, that can be determined from the initial values. This fully characterizes the long-time behaviour of the semigroup. Secondly, we show that the characterization of bad domains is equivalent to the Schiffer problem. This strengthens the conjecture that balls are the only bad domains and establishes a direct connection to geometric analysis. We also discuss implications for associated nonlinear systems.

math.AP↗
arXiv2025

Global existence and uniqueness for Hibler's visco-plastic sea-ice model

In this paper, we prove global existence and uniqueness of weak solutions to the momentum equations of Hibler's visco-plastic model for the dynamics of the arctic sea-ice covers. Although Hibler's model is standardly used in global climate simulations, there are only few rigorous mathematical results so far that mainly concern local-in-time well-posedness of globally regularized variants. Here, we consider Hibler's original model with local cut-off for arbitrarily small and large strain rates. Degeneracy and plasticity of the stress tensor hold in this range.

math.AP↗
arXiv2022

Global existence and convergence to pressure waves in nonlinear fluid-structure interaction

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and uniqueness for small data. At the same time, depending on the geometric setting, non-trivial time-periodic solutions, called pressure waves, may persist. Our main result is the characterization of long-time behaviour of the elastic displacement: up to small rigid motions, either the system comes to rest or converges to a pressure wave.

math.AP↗
arXiv2021

Rigorous Analysis and Dynamics of Hibler's sea ice model

This article develops for the first time a rigorous analysis of Hibler's model of sea ice dynamics. Identifying Hibler's ice stress as a quasilinear second order operator and regarding Hibler's model as a quasilinear evolution equation, it is shown that Hibler's coupled sea ice model, i.e., the model coupling velocity, thickness and compactness of sea ice, is locally strongly well-posed within the $L_q$-setting and also globally strongly well-posed for initial data close to constant equilibria.

math.AP↗
arXiv2020

Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems

We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface. Additional driving mechanisms can be included and non-smooth geometries and coefficients are admissible, to some extent. An important application are volume-surface reaction-diffusion systems with nonlinear coupled diffusion.

math.AP↗
arXiv2018

The 3D transient semiconductor equations with gradient-dependent and interfacial recombination

We establish the well-posedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: non-smooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on charge-carrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergence-form operators.

math.AP↗
arXiv2016

On maximal parabolic regularity for non-autonomous parabolic operators

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents $r\neq 2$. This allows us to prove maximal parabolic $L^r$-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations.

math.AP↗
arXiv2015

A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces

In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary, where diffusion coefficients are only assumed to be bounded, measurable and positive semidefinite. In the bulk, we additionally take into account diffusion coefficients which may degenerate towards a Lipschitz surface. For this problem class, we introduce a unified functional analytic framework based on sesquilinear forms and show maximal regularity for the corresponding abstract Cauchy problem.

math.AP↗
arXiv2014

Asymptotic behaviour of a rigid body with a cavity filled by a viscous liquid

We consider the system of equations modeling the free motion of a rigid body with a cavity filled by a viscous (Navier-Stokes) liquid. We give a rigorous proof of Zhukovskiy's Theorem, which states that in the limit of time going to infinity, the relative fluid velocity tends to zero and the rigid velocity of the full structure tends to a steady rotation around one of the principle axes of inertia. The existence of global weak solutions for this system was established previously. In particular, we prove that every weak solution of this type is subject to Zhukovskiy's Theorem. Independently of the geometry and of parameters, this shows that the presence of fluid prevents precession of the body in the limit. In general, we cannot predict which axis will be attained, but we show stability of the largest axis and provide criteria on the initial data which are decisive in special cases.

math.AP↗