42 citations · 252 across the 23 of their papers we have counts for
24 papers
The three limits of the hydrostatic approximation
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
The primitive equations are derived from the -Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an -thin domain and anisotropic viscosit…
Remark on the local well-posedness of compressible non-Newtonian fluids with initial vacuum
Hind Al Baba, Bilal Al Taki, Amru Hussein
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 stochastic primitive equations with non-isothermal turbulent pressure
Antonio Agresti, Matthias Hieber, Amru Hussein +1
In this paper, we introduce and study the primitive equations with -isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equatio…
The stochastic primitive equations with transport noise and turbulent pressure
Antonio Agresti, Matthias Hieber, Amru Hussein +1
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 ex…
Maximal -regularity and -calculus for block operator matrices and applications
Antonio Agresti, Amru Hussein
Many coupled evolution equations can be described via -block operator matrices of the form in a product space $…
The primitive equations with stochastic wind driven boundary conditions
Tim Binz, Matthias Hieber, Amru Hussein +1
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…
Hidden symmetries in non-self-adjoint graphs
Amru Hussein
On finite metric graphs the set of all realizations of the Laplace operator in the edgewise defined -spaces are studied. These are defined by coupling boundary conditions at t…
Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport
Matthias Hieber, Amru Hussein, Martin Saal
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…
If time were a graph, what would evolution equations look like?
Amru Hussein, Delio Mugnolo
Linear evolution equations are considered usually for the time variable being defined on an interval where typically initial conditions or time-periodicity of solutions are require…
Laplacians with point interactions -- expected and unexpected spectral properties
Amru Hussein, Delio Mugnolo
We study the one-dimensional Laplace operator with point interactions on the real line identified with two copies of the half-line . All possible boundary conditions th…
Primitive Equations with Horizontal Viscosity: The Initial Value and the Time-Periodic Problem for Physical Boundary Conditions
Amru Hussein, Martin Saal, Marc Wrona
The 3D-primitive equations with only horizontal viscosity are considered on a cylindrical domain , smooth, with the physical Dirichlet bo…
Partial and full hyper-viscosity for Navier-Stokes and primitive equations
Amru Hussein
The -D primitive equations and incompressible Navier-Stokes equations with full hyper-viscosity and only horizontal hyper-viscosity are considered on the torus, i.e., the diffus…
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
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 equat…
The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
Consider the -d primitive equations in a layer domain , , subject to mixed Dirichlet and Neumann boundary conditions at and , respectiv…
Primitive Equations with Linearly Growing Initial Data
Amru Hussein, Martin Saal, Okihiro Sawada
The primitive equations in a 3D infinite layer domain are considered with linearly growing initial data in the horizontal direction, which illustrates the global atmospheric rotati…
Analyticity of solutions to the primitive equations
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
This article presents the maximal regularity approach to the primitive equations. It is proved that the primitive equations on cylindrical domains admit a unique, global stron…
The Primitive Equations in the scaling invariant space
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
Consider the primitive equations on with initial data of the form , where and $a_2 \in L^\infty_σ(\R^2;L^1(…
Nematic Liquid Crystals in Lipschitz domains
Anupam Pal Choudhury, Amru Hussein, Patrick Tolksdorf
We consider the simplified Ericksen-Leslie model in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming…
Global Strong Well-Posedness of the 3D Primitive Equations with Heat and Salinity Diffusion
Matthias Hieber, Amru Hussein, Takahito Kashiwabara
Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown…
Non-self-adjoint graphs
Amru Hussein, David Krejcirik, Petr Siegl
On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral propert…
Sign-indefinite second order differential operators on finite metric graphs
Amru Hussein
The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn…
Maximal-quasi-accretive Laplacians on finite metric graphs
Amru Hussein
For a finite not necessarily compact metric graph, one considers the differential expression on each edge. The boundary conditions at the vertices of the graph…
Bounds on the negative eigenvalues of Laplacians on finite metric graphs
Amru Hussein
For a self--adjoint Laplace operator on a finite, not necessarily compact, metric graph lower and upper bounds on each of the negative eigenvalues are derived. For compact finite m…
Quantum graphs with mixed dynamics: the transport/diffusion case
Amru Hussein, Delio Mugnolo
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phen…