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Inhomogenous Navier--Stokes equations with unbounded density
Jean-Paul Adogbo, Piotr B. Mucha, Maja Szlenk
In the current state of the art regarding the Navier--Stokes equations, the existence of unique solutions for incompressible flows in two spatial dimensions is already well-establi…
Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment
Nilasis Chaudhuri, Jan Peszek, Maja Szlenk +1
We compare the multi-dimensional generalisation of the Aw-Rascle model with the pressureless Euler-alignment system, in which the communication weight is matrix-valued. Our general…
Construction of weak solutions to a pressureless viscous model driven by nonlocal attraction-repulsion
Piotr B. Mucha, Maja Szlenk, Ewelina Zatorska
We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existe…
Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids
Cosmin Burtea, Maja Szlenk
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tens…