Amru Hussein
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View article: The three limits of the hydrostatic approximation
The three limits of the hydrostatic approximation Open
The primitive equations are derived from the 3D Navier–Stokes equations by the hydrostatic approximation. Formally, assuming an ‐thin domain and anisotropic viscosities with vertical viscosity where , one obtains the primitive equations wi…
View article: The stochastic primitive equations with nonisothermal turbulent pressure
The stochastic primitive equations with nonisothermal turbulent pressure Open
In this paper, we introduce and study the primitive equations with nonisothermal turbulent pressure and transport noise. They are derived from the Navier–Stokes equations by employing stochastic versions of the Boussinesq and the hydrostat…
View article: Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum
Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum Open
We discuss in this short note the local-in-time strong well-posedness of the compressible Navier–Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, Mácha, and Ne…
View article: Strong Well-Posedness of the Q-Tensor Model for Liquid Crystals: The Case of Arbitrary Ratio of Tumbling and Aligning Effects $$\xi $$
Strong Well-Posedness of the Q-Tensor Model for Liquid Crystals: The Case of Arbitrary Ratio of Tumbling and Aligning Effects $$\xi $$ Open
The Beris–Edwards model of nematic liquid crystals couples an equation for the molecular orientation described by the Q-tensor with a Navier–Stokes type equation with an additional non-Newtonian stress caused by the molecular orientation. …
View article: The three limits of the hydrostatic approximation
The three limits of the hydrostatic approximation Open
The primitive equations are derived from the $3D$-Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an $\varepsilon$-thin domain and anisotropic viscosities with vertical viscosity $ν_z=\mathcal{O}(\varepsilon^γ)…
View article: Maximal L-regularity and H∞-calculus for block operator matrices and applications
Maximal L-regularity and H∞-calculus for block operator matrices and applications Open
Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ABCD] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered,…
View article: Remark on the local well-posedness of compressible non-Newtonian fluids with initial vacuum
Remark on the local well-posedness of compressible non-Newtonian fluids with initial vacuum Open
We discuss in this short note the local-in-time strong well-posedness of the compressible Navier-Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, Mácha, and Ne…
View article: The stochastic primitive equations with transport noise and turbulent pressure
The stochastic primitive equations with transport noise and turbulent pressure Open
In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic part…
View article: The stochastic primitive equations with non-isothermal turbulent pressure
The stochastic primitive equations with non-isothermal turbulent pressure Open
In this paper, we introduce and study the primitive equations with $\textit{non}$-isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and t…
View article: The stochastic primitive equations with transport noise and turbulent pressure
The stochastic primitive equations with transport noise and turbulent pressure Open
In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic part…
View article: Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications
Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications Open
Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix} A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the…
View article: Hidden symmetries in non-self-adjoint graphs
Hidden symmetries in non-self-adjoint graphs Open
On finite metric graphs the set of all realizations of the Laplace operator\nin the edgewise defined $L^2$-spaces are studied. These are defined by coupling\nboundary conditions at the vertices most of which define non-self-adjoint\noperat…
View article: If time were a graph, what would evolution equations look like?
If time were a graph, what would evolution equations look like? Open
Linear evolution equations are considered usually for the time variable being defined on an interval where typically initial conditions or time periodicity of solutions is required to single out certain solutions. Here, we would like to ma…
View article: Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions
Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions Open
The 3D-primitive equations with only horizontal viscosity are considered on a\ncylindrical domain $\\Omega=(-h,h) \\times G$, $G\\subset \\mathbb{R}^2$ smooth,\nwith the physical Dirichlet boundary conditions on the sides. Instead of\ncons…
View article: Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations*
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations* Open
Considering the anisotropic Navier–Stokes equations as well as the primitive equations, it is shown that the horizontal velocity of the solution to the anisotropic Navier–Stokes equations in a cylindrical domain of height ɛ with initial da…
View article: The primitive equations with stochastic wind driven boundary conditions
The primitive equations with stochastic wind driven boundary conditions Open
The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary…
View article: The primitive equations with stochastic wind driven boundary conditions: global strong well-posedness in critical spaces
The primitive equations with stochastic wind driven boundary conditions: global strong well-posedness in critical spaces Open
This article studies the primitive equations for geophysical flows subject to stochastic wind driven boundary conditions modeled by a cylindrical Wiener process. A rigorous treatment of stochastic boundary conditions yields that these equa…
View article: Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport
Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport Open
Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo transport subject to current noise, i.e., subject to stochastic forcing modeled by a cylindrical Wiener process. It is shown that this set of equations admits a u…
View article: Analyticity of solutions to the primitive equations
Analyticity of solutions to the primitive equations Open
This article presents the maximal regularity approach to the primitive equations. It is proved that the 3 D primitive equations on cylindrical domains admit a unique global strong solution for initial data lying in the critical solonoidal …
View article: Primitive equations with linearly growing initial data
Primitive equations with linearly growing initial data Open
The primitive equations in a 3D infinite layer domain are considered with\nlinearly growing initial data in the horizontal direction, which illustrates\nthe global atmospheric rotating or straining flows. On the boundaries,\nDirichlet, Neu…
View article: Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations Open
Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a cylindrical domain of height $\varepsilon $ with …
View article: Analyticity of solutions to the primitive equations
Analyticity of solutions to the primitive equations Open
This article presents the maximal regularity approach to the primitive equations. It is proved that the $3D$ primitive equations on cylindrical domains admit a unique, global strong solution for initial data lying in the critical solonoida…
View article: The Primitive Equations in the scaling invariant space $L^{\infty}(L^1)$
The Primitive Equations in the scaling invariant space $L^{\infty}(L^1)$ Open
Consider the primitive equations on $\R^2\times (z_0,z_1)$ with initial data $a$ of the form $a=a_1+a_2$, where $a_1 \in BUC_σ(\R^2;L^1(z_0,z_1))$ and $a_2 \in L^\infty_σ(\R^2;L^1(z_0,z_1))$ and where $BUC_σ(L^1)$ and $L^\infty_σ(L^1)$ den…