arXiv subjects

Flora Philipp

Publications and source records attributed to Flora Philipp.

2 recordsLinked to original sources

arXiv2026

Global existence analysis for a class of compressible Navier-Stokes-Korteweg equations

The existence of global weak solutions to a broad class of Navier-Stokes-Korteweg equations is established for large data in the three-dimensional torus, including the diffuse-interface and quantum Navier-Stokes systems as special cases. The model consists of the compressible Navier-Stokes equations with degenerate density-dependent viscosity and a general nonlinear third-order Korteweg term. The existence proof combines a priori estimates provided by the energy and Bresch-Desjardins (BD) entropy inequalities with a carefully designed approximation scheme. A crucial ingredient of the analysis is a new dissipation inequality associated with the Korteweg term, obtained via the systematic integration-by-parts method. To construct the solutions, artificial drag terms and a quantum Korteweg regularization are introduced, which are subsequently removed in the limit by establishing a renormalized formulation.

math.AP↗

arXiv2026

Chemotaxis compressible Navier-Stokes equations with density-dependent viscosity modeling vascular network formation

The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, is established in a three-dimensional torus for energy-finite initial data. The coupling of the equations arises through the chemotaxis force, which contributes to the momentum balance equation, and the signal production due to the cells in the chemotaxis equation. The equations model the self-assembly of endothelial cells during the early stages of blood vessel formation. The existence result holds for adiabatic pressure exponents $\gamma>4/3$, matching the exponent found in the existence analysis for the degenerate Keller-Segel equations. The proof leverages an approximation via Korteweg and drag terms, the BD entropy inequality, and a construction of weak solutions that are renormalized in the velocity variable.

math.AP↗