In this paper, we consider a coupled system of two nonlinearhyperbolic equations with variable-exponents in the damping and sourceterms. Under suitable assumptions on the intial data and the variableexponents, we prove a global existence theorem, using the Stable-setmethod. Then, we establish a decay estimate of the solution energy, byKomornik’s integral approach.

In this paper, we present a new technique for constructing a nonstationary wavelet. The key idea relies on the following: for each wavelet level, we solve the Bezout’s equation and we propose a positive solution over the interval [–1, 1]. Using the Bernstein’s polynomials we approximate this proposed positive solution with the intention to perform a spectral factorization.

In this paper, we present a new technique for constructing a nonstationary wavelet. The key idea relies on the following: for each wavelet level, we solve the Bezout’s equation and we propose a positive solution over the interval [–1, 1]. Using the Bernstein’s polynomials we approximate this proposed positive solution with the intention to perform a spectral factorization.

In this paper, we present a new technique for constructing a nonstationary wavelet. The key idea relies on the following: for each wavelet level, we solve the Bezout’s equation and we propose a positive solution over the interval [–1, 1]. Using the Bernstein’s polynomials we approximate this proposed positive solution with the intention to perform a spectral factorization.

In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result.

In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result.

In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result.

The current paper is principally motivated by establishing the global wellposedness to the three-dimensional Boussinesq system with zero diffusivity in thesetting of axisymmetric flows without swirling with v0 ∈ H12(R3) ∩ B˙ 30,1(R3) anddensity ρ0 ∈ L2(R3)∩B˙ 30,1(R3). This respectively enhances the two results recentlyaccomplished in Danchin and Paicu (2008) and Hmidi and Rousset (2010). Ourformalism is inspired, in particular for the first part from Abidi (2008) concerningthe axisymmetric Navier–Stokes equations once v0 ∈ H12(R3) and external forcef ∈ L2 loc(R+; Hβ(R3)), with β > 1 4 . This latter regularity on f which is thedensity in our context is helpless to achieve the global estimates for Boussinesqsystem. This technical defect forces us to deal once again with a similar proof tothat of Abidi (2008) but with f ∈ Lβ loc(R+; L2(R3)) for some β > 4. Second, weexplore the gained regularity on the density by considering it as an external forcein order to apply the study already obtained to the Boussinesq system.

The current paper is principally motivated by establishing the global wellposedness to the three-dimensional Boussinesq system with zero diffusivity in thesetting of axisymmetric flows without swirling with v0 ∈ H12(R3) ∩ B˙ 30,1(R3) anddensity ρ0 ∈ L2(R3)∩B˙ 30,1(R3). This respectively enhances the two results recentlyaccomplished in Danchin and Paicu (2008) and Hmidi and Rousset (2010). Ourformalism is inspired, in particular for the first part from Abidi (2008) concerningthe axisymmetric Navier–Stokes equations once v0 ∈ H12(R3) and external forcef ∈ L2 loc(R+; Hβ(R3)), with β > 1 4 . This latter regularity on f which is thedensity in our context is helpless to achieve the global estimates for Boussinesqsystem. This technical defect forces us to deal once again with a similar proof tothat of Abidi (2008) but with f ∈ Lβ loc(R+; L2(R3)) for some β > 4. Second, weexplore the gained regularity on the density by considering it as an external forcein order to apply the study already obtained to the Boussinesq system.

The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the classical two-dimensional and three-dimensional axisymmetric Navier-Stokes equations recently obtained in [19, 20]. Roughly speaking, we show essentially that if the initial data (v0; ρ0) is axisymmetricand (!0; ρ0) belongs to the critical space L1(Ω) ×L1(R3), with !0 is the initialvorticity associated to v0 and Ω = f(r; z) 2 R2 : r > 0g, then the viscousBoussinesq system has a unique global solution.

The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the classical two-dimensional and three-dimensional axisymmetric Navier-Stokes equations recently obtained in [19, 20]. Roughly speaking, we show essentially that if the initial data (v0; ρ0) is axisymmetricand (!0; ρ0) belongs to the critical space L1(Ω) ×L1(R3), with !0 is the initialvorticity associated to v0 and Ω = f(r; z) 2 R2 : r > 0g, then the viscousBoussinesq system has a unique global solution.

The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the classical two-dimensional and three-dimensional axisymmetric Navier-Stokes equations recently obtained in [19, 20]. Roughly speaking, we show essentially that if the initial data (v0; ρ0) is axisymmetricand (!0; ρ0) belongs to the critical space L1(Ω) ×L1(R3), with !0 is the initialvorticity associated to v0 and Ω = f(r; z) 2 R2 : r > 0g, then the viscousBoussinesq system has a unique global solution.

This papers deal with a new Adaptive Direct Power Control for Doubly-Fed Induction Generator of 1.5 MW. The main feature of the proposed strategy is based on the replacement of the fixed switching table by an adaptive one. The online update of the adaptive switching table depends on the reactive power variation and past switching sequences. The proposed adaptive direct power control is compared with Vector Control and Classical Direct Power Control. The robustness of the proposed control scheme against parameter, load and wind speed variations have done with success. The main performance of the Adaptive Direct Power Control strategy is the reduction of powers ripples, thus reduce of torque ripple on the shaft of the turbine.

This papers deal with a new Adaptive Direct Power Control for Doubly-Fed Induction Generator of 1.5 MW. The main feature of the proposed strategy is based on the replacement of the fixed switching table by an adaptive one. The online update of the adaptive switching table depends on the reactive power variation and past switching sequences. The proposed adaptive direct power control is compared with Vector Control and Classical Direct Power Control. The robustness of the proposed control scheme against parameter, load and wind speed variations have done with success. The main performance of the Adaptive Direct Power Control strategy is the reduction of powers ripples, thus reduce of torque ripple on the shaft of the turbine.

This papers deal with a new Adaptive Direct Power Control for Doubly-Fed Induction Generator of 1.5 MW. The main feature of the proposed strategy is based on the replacement of the fixed switching table by an adaptive one. The online update of the adaptive switching table depends on the reactive power variation and past switching sequences. The proposed adaptive direct power control is compared with Vector Control and Classical Direct Power Control. The robustness of the proposed control scheme against parameter, load and wind speed variations have done with success. The main performance of the Adaptive Direct Power Control strategy is the reduction of powers ripples, thus reduce of torque ripple on the shaft of the turbine.

This papers deal with a new Adaptive Direct Power Control for Doubly-Fed Induction Generator of 1.5 MW. The main feature of the proposed strategy is based on the replacement of the fixed switching table by an adaptive one. The online update of the adaptive switching table depends on the reactive power variation and past switching sequences. The proposed adaptive direct power control is compared with Vector Control and Classical Direct Power Control. The robustness of the proposed control scheme against parameter, load and wind speed variations have done with success. The main performance of the Adaptive Direct Power Control strategy is the reduction of powers ripples, thus reduce of torque ripple on the shaft of the turbine.

This papers deal with a new Adaptive Direct Power Control for Doubly-Fed Induction Generator of 1.5 MW. The main feature of the proposed strategy is based on the replacement of the fixed switching table by an adaptive one. The online update of the adaptive switching table depends on the reactive power variation and past switching sequences. The proposed adaptive direct power control is compared with Vector Control and Classical Direct Power Control. The robustness of the proposed control scheme against parameter, load and wind speed variations have done with success. The main performance of the Adaptive Direct Power Control strategy is the reduction of powers ripples, thus reduce of torque ripple on the shaft of the turbine.