16 citations · 17 across the 11 of their papers we have counts for
15 papers
The group of Symplectomorphisms of and the Euler equations
Hasan Inci
In this paper we consider the ``symplectic'' version of the Euler equations studied by Ebin \cite{ebin}. We show that these equations are globally well-posed on the Sobolev space $…
On the local well-posedness of the 1D Green-Naghdi system over a nonflat bottom
Hasan Inci
In this paper we consider the 1D Green-Naghdi system over a nonflat bottom. This system describes the evolution of water waves over an uneven bottom in the shallow water regime in…
On a Lagrangian formulation of the 1D Green-Naghdi system
Hasan Inci
In this paper we consider the 1D Green-Naghdi system. This system describes the evolution of water waves over a flat bottom in the shallow water regime in terms of the surface heig…
On the local well--posedness of the two component -family of equations
Hasan Inci
In this paper we consider the two component -family of equations on . We write the equations on a Sobolev type diffeomorphism group. As an application of this formula…
On the regularity of the solution map of the Euler-Poisson system
Hasan Inci
In this paper we consider the Euler-Poisson system (describing a plasma made of ions with a negligible ion temperature) on the Sobolev spaces , . Using a geomet…
Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
Hasan Inci, Y. Charles Li
We consider the incompressible 2D Euler equations on bounded spatial domain , and study the solution map on the Sobolev spaces (). Through an elaborate geometric…
On the regularity of the solution map of the porous media equation
Hasan Inci
In this paper we consider the incompressible porous media equation in the Sobolev spaces . We prove that for the time solution map …
On the well-posedness of the inviscid 2D Boussinesq equation
Hasan Inci
In this paper we consider the inviscid 2D Boussinesq equation on the Sobolev spaces , . Using a geometric approach we show that for any the corresponding…
On the well-posedness of the hyperelastic rod equation
Hasan Inci
In this paper we consider the hyperelastic rod equation on the Sobolev spaces , . Using a geometric approach we show that for any the corresponding soluti…
On the well-posedness of the inviscid SQG equation
Hasan Inci
In this paper we consider the inviscid SQG equation on the Sobolev spaces , . Using a geometric approach we show that for any the corresponding solution m…
On the well-posedness of the Holm-Staley b-family of equations
Hasan Inci
In this paper we consider the Holm-Staley -family of equations in the Sobolev spaces for . Using a geometric approach we show that, for any value of th…
On the regularity of the solution map of the incompressible Euler equation
Hasan Inci
In this paper we consider the incompressible Euler equation on the Sobolev space , , and show that for any its solution map , mappin…
On the well-posedness of the incompressible Euler Equation
Hasan Inci
In this thesis we prove that the homogeneous incompressible Euler equation of hydrodynamics on the Sobolev spaces , and , can be expressed as a geo…
On a Lagrangian formulation of the incompressible Euler equation
Hasan Inci
In this paper we show that the incompressible Euler equation on the Sobolev space , , can be expressed in Lagrangian coordinates as a geodesic equation on an…
On the regularity of the composition of diffeomorphisms
Hasan Inci, Thomas Kappeler, Peter Topalov
For being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of -regular diffeomorphisms of for $s > 1/2\…