arXiv subjects

Pierre Marie Ngougoue Ngougoue

Publications and source records attributed to Pierre Marie Ngougoue Ngougoue.

3 recordsLinked to original sources

arXiv2026

Blow-Up Criteria and Weak--Strong Uniqueness for Compressible Fluid--Viscoelastic Shell Interactions

Existence and uniqueness of strong solutions to a barotropic compressible fluid--viscoelastic shell interaction system have recently been established on a finite time interval. A natural question is whether such solutions can be continued globally. In this work, we derive a continuation criterion for this coupled system. Our analysis is based on an energy estimate at the level of material acceleration, derived under Serrin-type and Beale--Kato--Majda-type control assumptions. While in the incompressible setting, such control is sufficient to prevent finite-time blow-up, in the compressible regime it does not by itself ensure propagation of the full regularity required for strong solutions. To obtain a genuine continuation criterion, we impose a Beale--Kato--Majda Lipschitz-type control on the density and velocity gradients with stronger time integrability. In combination with the control framework underlying the acceleration estimate, we close a higher-order energy estimate and thereby prevent loss of strong-solution regularity. Consequently, the solution can be extended beyond a potential blow-up time, provided that the corresponding control norms remain finite. We further establish a weak-strong uniqueness principle for the system under the above conditional regularity criterion.

math.AP↗

arXiv2026

Stochastically-constrained Koiter shell models

We derive stochastically-constrained Koiter shell models in line with the SALT (Stochastic Advection by Lie Transport) approach introduced by Holm [Proc. A. 471 (2015)]. First, we deduce the stochastic partial differential equations for the generalised nonlinear elastic and linear elastic Koiter shell models with abstract functional derivatives of their corresponding membrane and flexural energies. We then present a prototype for a stochastically-constrained (simplified) linearised Koiter shell model that captures stiffness effects arising from shell curvature, bending and membrane stresses, interior and surface forces, and, more generally, stochastic buckling. Finally, we show that if a weak pathwise solution of this prototype is parametrised by a suitably chosen family of noise coefficients, we obtain in the parameter limit, the deterministic viscoelastic shell model with viscous damping.

math.AP↗

arXiv2025

Local Well-Posedness For Barotropic Compressible Fluid-Viscoelastic Shell Interactions

We study a three-dimensional barotropic compressible Navier-Stokes flow interacting with a viscoelastic shell that occupies a portion of the fluid boundary. The analysis is entirely Eulerian and the moving interface is parametrised by a localised Hanzawa transform supported near the shell patch, which preserves the transport structure of the continuity equation and avoids a global Lagrangian map. We prove local-in-time existence and uniqueness of strong solutions for compatible data and without imposing a vanishing initial shell displacement. The proof combines a well-posedness theory for the continuity equation, solved by the method of characteristics in the Hanzawa frame, with an analysis of the momentum-structure subproblem carried out by the classical linearisation-energy estimate -- fixed-point scheme on a fixed reference domain. A Banach fixed point then couples the two steps and closes the argument on a short time interval. We work with a viscosity-weighted energy that makes the scaling in the shear and bulk viscosities explicit. This yields bounds whose constants grow at most linearly in these parameters. In particular, the estimates are inviscid-limit compatible. The result complements the global finite-energy weak theory for compressible fluid-shell interaction by providing a local strong well-posedness statement in the same geometric configuration. It also extends strong boundary results beyond beams and plates to bending shells, and addresses the wave-to-bending direction suggested in the literature on compressible fluid-structure interaction at structural boundaries, while remaining fully Eulerian.

math.AP↗