| RESEARCHANNOUNCEMENTS——TheCauchyProblemsandGlobalSolutionstoDeybeSystemandBurgers'EquationsinPseudomeasureSpaces |
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| 引用本文： | 原保全.RESEARCHANNOUNCEMENTS——TheCauchyProblemsandGlobalSolutionstoDeybeSystemandBurgers''''EquationsinPseudomeasureSpaces[J].数学进展,2004(6). |
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| 作者姓名： | 原保全 |
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| 作者单位： | Beijing Graduate |
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| 基金项目： | foundationitem:ThisworkispartlysupportedbytheNationalNaturalScienceFoundationofChinaandtheScienceFoundationfortheExcellentYoungTeacherofHenanProvince. |
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| 摘 要： | In this paper we consider the construction of solutions to the Cauchy problem of Burgers' equationsut-γ△u + u·▽u = 0, t∈R+,x∈R3, (1)u(0,x)= u0(x), x ∈ R3, (2)in pseudomeasure spaces, where γ(?) 0 is a small parameter that plays the role of the viscosity and u = u(t,x) is a velocity-like vector field defined on R+×R3. The initial datum u0(x) is a vector-valued function defined on R3, In one space dimension Burgers' equation is
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