TY - CHAP
T1 - Existence, Uniqueness and Regularity for the Second-Gradient Navier-Stokes Equations in Exterior Domains
AU - Degiovanni, Marco
AU - Marzocchi, Alfredo
AU - Mastaglio, Sara
PY - 2021
Y1 - 2021
N2 - We study the well-posedness of the problem
⎧
⎪
⎨
⎪
⎩
∂u
∂t
+ (Du)u + ∇p = νΔu − τΔΔu in ]0,+∞[×Ω,
divu = 0 in ]0,+∞[×Ω,
u(t,x) =
∂u
∂n (t,x) = 0
on ]0,+∞[×∂Ω,
u(0,x) = u 0 (x) in Ω,
where u :]0,+∞[×Ω → R n is the velocity field, p :]0,+∞[×Ω → R is the pressure,
ν is the kinematical viscosity, τ the so-called hyperviscosity and Ω is a general
domain as for existence and uniqueness of the solution, and an exterior domain as
for regularity results.
This problem has been physically well motivated in the recent years as the
simplest case of an isotropic second-order fluid, i.e. a fluid whose power expended
depends on second derivatives of the velocity field.
AB - We study the well-posedness of the problem
⎧
⎪
⎨
⎪
⎩
∂u
∂t
+ (Du)u + ∇p = νΔu − τΔΔu in ]0,+∞[×Ω,
divu = 0 in ]0,+∞[×Ω,
u(t,x) =
∂u
∂n (t,x) = 0
on ]0,+∞[×∂Ω,
u(0,x) = u 0 (x) in Ω,
where u :]0,+∞[×Ω → R n is the velocity field, p :]0,+∞[×Ω → R is the pressure,
ν is the kinematical viscosity, τ the so-called hyperviscosity and Ω is a general
domain as for existence and uniqueness of the solution, and an exterior domain as
for regularity results.
This problem has been physically well motivated in the recent years as the
simplest case of an isotropic second-order fluid, i.e. a fluid whose power expended
depends on second derivatives of the velocity field.
KW - Fluid Mechanics
KW - Navier-Stokes equations
KW - Fluid Mechanics
KW - Navier-Stokes equations
UR - http://hdl.handle.net/10807/201701
U2 - 10.1007/978-3-030-68144-9
DO - 10.1007/978-3-030-68144-9
M3 - Chapter
SN - 978-3-030-68143-2
SP - 181
EP - 202
BT - Waves in Flows
A2 - Bodnar, Tomaš
A2 - Galdi, Giovanni P.
A2 - Nečasová, Šarka
ER -