Work

Blow-up criterion for the compressible Navier–Stokes system with inflow-outflow boundary conditions

Year: 2026

Type: article

Abstract: We consider the compressible Navier-Stokes system in three dimensions with general inflow-outflow boundary conditions, meaning that we prescribe a boundary velocity which has a negative normal component and accordingly the density is prescribed on the inflow part of the boundary. We establish a blow-up criterion in a class of strong solutions in the $$L^p-L^q$$ L p - L q framework. In particular assuming the boundedness of the quantities $$(\varrho ^{-1}, \varvec{u})$$ ( ϱ - 1 , u ) and of a suitable norm of $$\nabla _x \varrho $$ ∇ x ϱ the solution remains regular and the blow-up does not occur. We develop the condition on $$\nabla _x \varrho $$ ∇ x ϱ because we need a new approach in order to accommodate the inhomogeneous boundary conditions, as the standard estimates on the material time derivative work when the normal component of the boundary velocity is zero.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-026-01235-x

Authors: Anna Abbatiello, Mostafa Meliani

Institutions: University of Campania "Luigi Vanvitelli", University of Bath

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Grantová Agentura České Republiky, Akademie Věd České Republiky, Gruppo Nazionale per la Fisica Matematica