Existence and stability of global solutions to a regularized Oldroyd-B model in its vorticity formulation

Jaracz, Jaroslaw S.; Lee, Young Ju

doi:10.1016/j.jde.2022.04.027

Cited by 3 publications

(3 citation statements)

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“…We comment that though justifiable, the introduction of the modified term in our equations could be considered somewhat ad-hoc, though no more so than in [4]. As mentioned, in that paper, and others, the modifications are introduced by considering Brownian motion, while here we introduced them as a consequence of special and general relativity.…”

Section: Discussionmentioning

confidence: 95%

“…In a recent paper [4] we studied a modified model of visco-elastic fluids. Based on physical and experimental observations, one of the modifications to the ordinary model was the change…”

Section: Introductionmentioning

confidence: 99%

“…Thus the solutions to this system should yield a good approximation to the solutions of the ordinary Navier-Stokes equations under physically reasonable conditions. The modification of the convective term is a natural progression of the work done in [4]. The property that |v| ≤ c embodies the notion that in relativity matter can't travel faster than the speed of light, giving the model its name.…”

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confidence: 99%

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The Global Existence of Solutions to a Quasi-Relativistic Incompressible Navier-Stokes Model

Jaracz¹

2022

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We introduce a new modified Navier-Stokes model in 3 dimensions by modifying the convection term in the ordinary Navier-Stokes equations. This is done by replacing the convective term (u • ∇)u by (v • ∇)u with v = cu/ c 2 + |u| 2 where c is the speed of light. Thus we have that |v| ≤ c and for |u| ≪ c we have v ≈ u. Thus the solutions to this system should yield a good approximation to the solutions of the ordinary Navier-Stokes equations under physically reasonable conditions. The modification of the convective term is a natural progression of the work done in [4]. The property that |v| ≤ c embodies the notion that in relativity matter can't travel faster than the speed of light, giving the model its name. We prove that there exists a strong solution u ∈ L 2 (0, T ; H 2 )∩L ∞ (0, T ; V) with u ′ ∈ L 2 (0, T ; L 2 ) to our system of equations on either a smooth bounded domain U ⊂ R 3 or the flat 3-torus T for any initial velocity u 0 ∈ V and any forcing function f ∈ L 2 (0, T ; L 2 ). No assumption on the smallness of the data is necessary. Here V is the space of weakly divergence free vector fields with components in H 1 which vanish on the boundary. We also prove the uniqueness of this strong solution. Though our modification is somewhat ad-hoc, it suggests that though more complicated, equations incorporating aspects of special and general relativity might have better existence and uniqueness properties than the ordinary Navier-Stokes equations.

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Section: Discussionmentioning

confidence: 95%

“…In a recent paper [4] we studied a modified model of visco-elastic fluids. Based on physical and experimental observations, one of the modifications to the ordinary model was the change…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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