Global stability in the B�nard problem for a mixture with superimposed plane parallel shear flows

Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

“…A nonlinear energy stability analysis is really beneficial when it can be used to provide stability thresholds close to those of linear theory and valid for all initial conditions,as emphasized by Straughan (p. 157 of [19]). Many recent studies have focussed upon this problem (see Payne and Straughan [17], Budu [20], Lombardo et al [21], Straughan [22]). Flavin and Rionero [12][13][14] utilized the 'natural' transformation to deal with when the thermal conductivity is a nonlinear function of temperature, at least with regard to a particular class of nonlinearity.…”

Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

“…A nonlinear energy stability analysis is really beneficial when it can be used to provide stability thresholds close to those of linear theory and valid for all initial conditions,as emphasized by Straughan (p. 157 of [19]). Many recent studies have focussed upon this problem (see Payne and Straughan [17], Budu [20], Lombardo et al [21], Straughan [22]). Flavin and Rionero [12][13][14] utilized the 'natural' transformation to deal with when the thermal conductivity is a nonlinear function of temperature, at least with regard to a particular class of nonlinearity.…”

A new approach to nonlinear L2-stability of double diffusive convection in porous media: Necessary and sufficient conditions for global stability via a linearization principle

“…The stability of (6) has been considered by several authors (also when rotation about the vertical axis is incorporated) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Precisely, denoting by (i) are periodic in the x and y directions respectively of periods 2π a x and 2π a y , (ii) on the periodicity cell Ω = [0, 2π a x ] × [0, 2π a y ] × [0, 1] (in order to guarantee uniqueness) u and v have zero mean value, (iii) belong to L 2 (Ω), ∀t ∈ R + , the results on nonlinear energy stability [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as far as we know, can be summarized as follows: there exists a bounded positive number R * ∞ such that…”

Sharp global nonlinear stability for temperature-dependent viscosity convection

“…Several recent articles have explicitly addressed this question in a variety of contexts (cf. Flavin & Rionero 1998, 1999aLombardo et al . 2000;Payne & Straughan 2000;Straughan 2001).…”

Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

“…A nonlinear energy stability analysis is really beneficial when it can be used to provide stability thresholds close to those of linear theory and valid for all initial conditions,as emphasized by Straughan (p. 157 of [19]). Many recent studies have focussed upon this problem (see Payne and Straughan [17], Budu [20], Lombardo et al [21], Straughan [22]). Flavin and Rionero [12][13][14] utilized the 'natural' transformation to deal with when the thermal conductivity is a nonlinear function of temperature, at least with regard to a particular class of nonlinearity.…”

A new approach to nonlinear L2-stability of double diffusive convection in porous media: Necessary and sufficient conditions for global stability via a linearization principle

“…The stability of (6) has been considered by several authors (also when rotation about the vertical axis is incorporated) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Precisely, denoting by (i) are periodic in the x and y directions respectively of periods 2π a x and 2π a y , (ii) on the periodicity cell Ω = [0, 2π a x ] × [0, 2π a y ] × [0, 1] (in order to guarantee uniqueness) u and v have zero mean value, (iii) belong to L 2 (Ω), ∀t ∈ R + , the results on nonlinear energy stability [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as far as we know, can be summarized as follows: there exists a bounded positive number R * ∞ such that…”

Sharp global nonlinear stability for temperature-dependent viscosity convection

“…Several recent articles have explicitly addressed this question in a variety of contexts (cf. Flavin & Rionero 1998, 1999aLombardo et al . 2000;Payne & Straughan 2000;Straughan 2001).…”

Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

“…A nonlinear energy stability analysis is really beneficial when it can be used to provide stability thresholds close to those of linear theory and valid for all initial conditions,as emphasized by Straughan (p. 157 of [19]). Many recent studies have focussed upon this problem (see Payne and Straughan [17], Budu [20], Lombardo et al [21], Straughan [22]). Flavin and Rionero [12][13][14] utilized the 'natural' transformation to deal with when the thermal conductivity is a nonlinear function of temperature, at least with regard to a particular class of nonlinearity.…”

A new approach to nonlinear L2-stability of double diffusive convection in porous media: Necessary and sufficient conditions for global stability via a linearization principle

“…The stability of (6) has been considered by several authors (also when rotation about the vertical axis is incorporated) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Precisely, denoting by (i) are periodic in the x and y directions respectively of periods 2π a x and 2π a y , (ii) on the periodicity cell Ω = [0, 2π a x ] × [0, 2π a y ] × [0, 1] (in order to guarantee uniqueness) u and v have zero mean value, (iii) belong to L 2 (Ω), ∀t ∈ R + , the results on nonlinear energy stability [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as far as we know, can be summarized as follows: there exists a bounded positive number R * ∞ such that…”

Sharp global nonlinear stability for temperature-dependent viscosity convection

“…Several recent articles have explicitly addressed this question in a variety of contexts (cf. Flavin & Rionero 1998, 1999aLombardo et al . 2000;Payne & Straughan 2000;Straughan 2001).…”