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Papers by Tesfalem Abate Tegegn

arXiv: Analysis of PDEs, Sep 3, 2021

The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theor... more The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; $ -3/2 $ is the spectral slope in Kraichnan-Iroshnikov-Dobrowolny (KID) theory, $ -5/3 $ in Marsch-Matthaeus-Zhou's and Goldreich-Sridhar theories also called Kolmogorov-like (K-41 like) MHD theory, combination of the −5/3-5/3−5/3 and −3/2-3/2−3/2 scales in Biskamp and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig [Physica D 241(2012) 426-438], we establish inertial range bounds for K-41 like phenomenon in MHD turbulent flow through a mathematical rigour; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to −5/3-5/3−5/3 is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its average over time decreases in time.

Turbulence in fluids is a routine phenomenon in nature. It has fascinated scientists over the age... more Turbulence in fluids is a routine phenomenon in nature. It has fascinated scientists over the ages and remains one of the greatest challenges of modern science. Based on works of Taylor, Von Karman, Horward, Millionschikov and Obukhov, and using essentially similarity transformations (scaling arguments), Kolmogorov stated in 1941 striking hypotheses regarding the behavior of the spectral energy of fluids in turbulent regimes governed by Navier-Stoke's equations; his theory is known as K41. The analog of K41 for magnetohydrodynamics(MHD) flows was elaborated by Kraichnan and Iroshnikov in the early 1960's. Of great scientific interest is the question of rigorous mathematical proof of Kolmogorov's hypotheses under physically acceptable conditions. Biryuk and Craig in 2012, obtained interesting results in that direction for fluids governed by Navier-Stokes equations. In view of the prevalence of MHD fluids across the spectrum of important phenomena, from Astrophysics to Nuc...

In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-α ... more In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-α Navier-Stokes model on the two dimensional torus. We assume that the noise is a cylindrical Wiener process and its coefficient is multiplied by √ α. We then study through the lenses of the large and moderate deviations principle the behaviour of the trajectories of the solutions of the stochastic system as α goes to 0. Instead of giving two separate proofs of the two deviations principles we present a unifying approach to the proof of the LDP and MDP and express the rate function in term of the unique solution of the NavierStokes equations. Our proof is based on the weak convergence approach to large deviations principle. As a by-product of our analysis we also prove that the solutions of the stochastic LANS-α model converge in probability to the solutions of the deterministic Navier-Stokes equations.

This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) t... more This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) turbulence flows. Part I consists of introduction and background (or preliminary) materials which were crucially important in the process. The main body of the thesis is included in parts II and III. In Part II, new regularity results for stochastic heat equations in probabilistic evolution spaces of Besov type are established, which in turn were used to establish global and local in time existence and uniqueness results for stochastic MHD equations. The existence result holds with positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools, such as Littlewood-Paley decomposition, Jean-Micheal Bony paradifferential calculus and stochastic calculus. Our global existence result is new in three-dimensional spaces and is published in [148](Sango and Tegegn, Harmonic analysis tools for stochastic magnetohydrodynamics equations in...

The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theor... more The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; −3/2 is the spectral slope in Kraichnan-IroshnikovDobrowolny (KID) theory, −5/3 in Marsch-Matthaeus-Zhou’s and Goldreich-Sridhar theories also called Kolmogorov-like (K-41 like) MHD theory, combination of the −5/3 and −3/2 scales in Biskamp and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig [Physica D 241(2012) 426-438], we establish inertial range bounds for K-41 like phenomenon in MHD turbulent flow through a mathematical rigour; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to −5/3 is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its ...

International Journal of Data and Network Science, 2021

This paper investigates the impact of post-purchase user generated content (UGC) and traditional ... more This paper investigates the impact of post-purchase user generated content (UGC) and traditional reference groups on the purchase intentions for electronic products (e-products) among young consumers in Jordan. To achieve this, a descriptive methodology was adapted, with a quantitative approach and survey strategy utilizing a five-point Likert scale questionnaire distributed to 450 university and college students in Jordan. 400 filtered and screened copies underwent statistical analyses. SPSS version 21 was utilized to describe and analyze the data. The results revealed a strong impact of post-purchase UGC on purchase intentions of e-products among young consumers. The results also revealed that traditional reference groups have a lower significant impact on the purchase intentions of young consumers, indicating that young consumers rely on online communities more than they rely on family, friends, colleagues, and other social organizations. The findings are discussed with a view to...

International Journal of Modern Physics B, 2016

We establish a regularity result for stochastic heat equations in probabilistic evolution spaces ... more We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.

arXiv: Analysis of PDEs, Sep 3, 2021

The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theor... more The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; $ -3/2 $ is the spectral slope in Kraichnan-Iroshnikov-Dobrowolny (KID) theory, $ -5/3 $ in Marsch-Matthaeus-Zhou's and Goldreich-Sridhar theories also called Kolmogorov-like (K-41 like) MHD theory, combination of the −5/3-5/3−5/3 and −3/2-3/2−3/2 scales in Biskamp and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig [Physica D 241(2012) 426-438], we establish inertial range bounds for K-41 like phenomenon in MHD turbulent flow through a mathematical rigour; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to −5/3-5/3−5/3 is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its average over time decreases in time.

Turbulence in fluids is a routine phenomenon in nature. It has fascinated scientists over the age... more Turbulence in fluids is a routine phenomenon in nature. It has fascinated scientists over the ages and remains one of the greatest challenges of modern science. Based on works of Taylor, Von Karman, Horward, Millionschikov and Obukhov, and using essentially similarity transformations (scaling arguments), Kolmogorov stated in 1941 striking hypotheses regarding the behavior of the spectral energy of fluids in turbulent regimes governed by Navier-Stoke's equations; his theory is known as K41. The analog of K41 for magnetohydrodynamics(MHD) flows was elaborated by Kraichnan and Iroshnikov in the early 1960's. Of great scientific interest is the question of rigorous mathematical proof of Kolmogorov's hypotheses under physically acceptable conditions. Biryuk and Craig in 2012, obtained interesting results in that direction for fluids governed by Navier-Stokes equations. In view of the prevalence of MHD fluids across the spectrum of important phenomena, from Astrophysics to Nuc...

In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-α ... more In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-α Navier-Stokes model on the two dimensional torus. We assume that the noise is a cylindrical Wiener process and its coefficient is multiplied by √ α. We then study through the lenses of the large and moderate deviations principle the behaviour of the trajectories of the solutions of the stochastic system as α goes to 0. Instead of giving two separate proofs of the two deviations principles we present a unifying approach to the proof of the LDP and MDP and express the rate function in term of the unique solution of the NavierStokes equations. Our proof is based on the weak convergence approach to large deviations principle. As a by-product of our analysis we also prove that the solutions of the stochastic LANS-α model converge in probability to the solutions of the deterministic Navier-Stokes equations.

This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) t... more This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) turbulence flows. Part I consists of introduction and background (or preliminary) materials which were crucially important in the process. The main body of the thesis is included in parts II and III. In Part II, new regularity results for stochastic heat equations in probabilistic evolution spaces of Besov type are established, which in turn were used to establish global and local in time existence and uniqueness results for stochastic MHD equations. The existence result holds with positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools, such as Littlewood-Paley decomposition, Jean-Micheal Bony paradifferential calculus and stochastic calculus. Our global existence result is new in three-dimensional spaces and is published in [148](Sango and Tegegn, Harmonic analysis tools for stochastic magnetohydrodynamics equations in...

The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theor... more The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; −3/2 is the spectral slope in Kraichnan-IroshnikovDobrowolny (KID) theory, −5/3 in Marsch-Matthaeus-Zhou’s and Goldreich-Sridhar theories also called Kolmogorov-like (K-41 like) MHD theory, combination of the −5/3 and −3/2 scales in Biskamp and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig [Physica D 241(2012) 426-438], we establish inertial range bounds for K-41 like phenomenon in MHD turbulent flow through a mathematical rigour; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to −5/3 is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its ...

International Journal of Data and Network Science, 2021

This paper investigates the impact of post-purchase user generated content (UGC) and traditional ... more This paper investigates the impact of post-purchase user generated content (UGC) and traditional reference groups on the purchase intentions for electronic products (e-products) among young consumers in Jordan. To achieve this, a descriptive methodology was adapted, with a quantitative approach and survey strategy utilizing a five-point Likert scale questionnaire distributed to 450 university and college students in Jordan. 400 filtered and screened copies underwent statistical analyses. SPSS version 21 was utilized to describe and analyze the data. The results revealed a strong impact of post-purchase UGC on purchase intentions of e-products among young consumers. The results also revealed that traditional reference groups have a lower significant impact on the purchase intentions of young consumers, indicating that young consumers rely on online communities more than they rely on family, friends, colleagues, and other social organizations. The findings are discussed with a view to...

International Journal of Modern Physics B, 2016

We establish a regularity result for stochastic heat equations in probabilistic evolution spaces ... more We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.