Researcher:
İnci, Hasan

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Hasan

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İnci

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İnci, Hasan

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2018 - 201942020 - 20211

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Researcher Of Publications: search.filters.isAuthorOfPublication.14e6d3a4-fc3d-4c7d-9ee1-5f5182a928e0

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    On the well-posedness of the hyperelastic rod equation
    (Springer Heidelberg, 2019) N/A; Department of Mathematics; İnci, Hasan; Faculty Member; Department of Mathematics; College of Sciences; 274184
    In this paper we consider the hyperelastic rod equation on the Sobolev spaces Hs(R), s>3/2. Using a geometric approach we show that for any T>0 the corresponding solution map, u(0)?u(T), is nowhere locally uniformly continuous. The method applies also to the periodic case Hs(T), s>3/2.
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    On the well-posedness of the inviscid 2D Boussinesq equation
    (Birkhauser Verlag Ag, 2018) Department of Mathematics; İnci, Hasan; Faculty Member; Department of Mathematics; College of Sciences; 274184
    In this paper, we consider the inviscid 2D Boussinesq equation on the Sobolev spaces Hs(R2), s > 2. Using a geometric approach, we show that for any T > 0 the corresponding solution map, (u(0),theta(0))-> (u(T),theta(T)), is nowhere locally uniformly continuous.
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    On the regularity of the solution map of the Euler-Poisson system
    (TÜBİTAK, 2019) Department of Mathematics; İnci, Hasan; Department of Mathematics; College of Sciences; 274184
    In this paper we consider the Euler-Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces H-s(R-3) , s > 5/2. Using a geometric approach we show that for any time T > 0 the corresponding solution map, (rho(0), u(0)) bar right arrow (rho(T), u(T)) , is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in R-3.
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    On the local well-posedness of the two component b-family of equations
    (Springer, 2021) Department of Mathematics; İnci, Hasan; Department of Mathematics; College of Sciences; 274184
    In this paper we consider the two component b-family of equations on R. We write the equations on a Sobolev type diffeomorphism group. As an application of this formulation we show that the dependence on the initial data is nowhere locally uniformly continuous. In particular it is nowhere locally Lipschitz and nowhere locally Holder continuous.
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    Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
    (International Press of Boston, 2019) Li, Y. Charles; Department of Mathematics; İnci, Hasan; Department of Mathematics; College of Sciences; 274184
    We consider the incompressible 2D Euler equations on bounded spatial domain S, and study the solution map on the Sobolev spaces H-k(S) (k > 2). Through an elaborate geometric construction, we show that for any T > 0, the time T solution map u(0) bar right arrow u(T) is nowhere locally uniformly continuous and nowhere Frechet differentiable.