In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for ...In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.展开更多
In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and...In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.展开更多
The secular variations (SV) in g01 of geomagnetic field, caused by the interaction between the geomagnetic field and the radial fluid-flow of the outer-core, are discussed with both statistical and analytic methods. W...The secular variations (SV) in g01 of geomagnetic field, caused by the interaction between the geomagnetic field and the radial fluid-flow of the outer-core, are discussed with both statistical and analytic methods. When the value of g01 s02 is relatively high compared with other terms, SV in g01 is characterized by exponential change. When the effect of non-dipole field is notable, SV in g01 shows complex features. Especially when the value of g01 is close to zero, SV in g01 is completely determined by the random process of non-dipole fields.展开更多
基金supported by the Zhejiang Natural Science Foundation of China(LQ13A010022)supported by the Qianjiang professorship of Zhejiang Province of Chinathe National Natural Science Foundation of China(11271105)
文摘In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.
文摘In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 49429405) by the Chinese Academy of Sciences
文摘The secular variations (SV) in g01 of geomagnetic field, caused by the interaction between the geomagnetic field and the radial fluid-flow of the outer-core, are discussed with both statistical and analytic methods. When the value of g01 s02 is relatively high compared with other terms, SV in g01 is characterized by exponential change. When the effect of non-dipole field is notable, SV in g01 shows complex features. Especially when the value of g01 is close to zero, SV in g01 is completely determined by the random process of non-dipole fields.