Well-Posedness of the Stochastic Transport Equation with Unbounded Drift

被引：4
|
作者：
Mollinedo, David A. C. [1 ]
Olivera, Christian [2 ]
机构：
[1] Univ Tecnol Fed Parana, Curitiba, Parana, Brazil
[2] Univ Estadual Campinas, Dept Matemat, Campinas, SP, Brazil
来源：
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2017年 / 48卷 / 04期
基金：
巴西圣保罗研究基金会;
关键词：
Stochastic partial differential equation; Transport equation; Low regularity; Stochastic characteristic method; BV VECTOR-FIELDS;
D O I：
10.1007/s00574-017-0039-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based on a careful analysis of the associated stochastic flow of characteristics and techniques of stochastic analysis.
引用
收藏
页码：663 / 677
页数：15
相关论文
共 50 条
  • [41] The well-posedness problem of a hyperbolic-parabolic mixed type equation on an unbounded domain
    Zhan, Huashui
    ANALYSIS AND MATHEMATICAL PHYSICS, 2019, 9 (04) : 1849 - 1864
  • [42] WELL-POSEDNESS FOR THE SUPERCRITICAL GKDV EQUATION
    Strunk, Nils
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (02) : 527 - 542
  • [43] On well-posedness for the Benjamin–Ono equation
    Nicolas Burq
    Fabrice Planchon
    Mathematische Annalen, 2008, 340 : 497 - 542
  • [44] Sharp well-posedness for the Benjamin equation
    Chen, W.
    Guo, Z.
    Xiao, J.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) : 6209 - 6230
  • [45] On the Gevrey well-posedness of the Kirchhoff equation
    Tokio Matsuyama
    Michael Ruzhansky
    Journal d'Analyse Mathématique, 2019, 137 : 449 - 468
  • [46] Well-posedness for a perturbation of the KdV equation
    X. Carvajal
    L. Esquivel
    Nonlinear Differential Equations and Applications NoDEA, 2019, 26
  • [47] On the well-posedness of the hyperelastic rod equation
    Hasan Inci
    Annali di Matematica Pura ed Applicata (1923 -), 2019, 198 : 795 - 802
  • [48] On the well-posedness of Galbrun's equation
    Hagg, Linus
    Berggren, Martin
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2021, 150 : 112 - 133
  • [49] Well-Posedness of a Parabolic Equation with Involution
    Ashyralyev, Allaberen
    Sarsenbi, Abdizhahan
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (10) : 1295 - 1304
  • [50] LOCAL WELL-POSEDNESS FOR KAWAHARA EQUATION
    Kato, Takamori
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2011, 16 (3-4) : 257 - 287
12345