SUPPRESSION OF BLOW UP BY MIXING IN GENERALIZED KELLER-SEGEL SYSTEM WITH FRACTIONAL DISSIPATION

被引：0

作者：

Shi, Binbin ^{[1
]}

Wang, Weike ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai 200240, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2020年 / 18卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Generalized Keller-Segel system; Mixing; Fractional dissipation; Suppression of blow up; MAXIMUM PRINCIPLE; GLOBAL EXISTENCE; DIFFUSION; MODEL; FLOWS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with a fractional dissipation and an additional mixing effect of advection by an incompressible flow. Under a suitable mixing condition on the advection, we study well-posedness of solution with large initial data. We establish the global L-infinity estimate of the solution through nonlinear maximum principle, and obtain the global existence of classical solution.

引用

页码：1413 / 1440

页数：28

共 36 条

[1] An approximate treatment of gravitational collapse [J].

Ascasibar, Yago ;

Granero-Belinchon, Rafael ;

Manuel Moreno, Jose .

PHYSICA D-NONLINEAR PHENOMENA, 2013, 262 :71-82

[2] SUPPRESSION OF BLOW-UP IN PATLAK-KELLER-SEGEL VIA SHEAR FLOWS [J].

Bedrossian, Jacob ;

He, Siming .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (06) :4722-4766

[3] The Sobolev inequality on the torus revisited [J].

Benyi, Arpad ;

Oh, Tadahiro .

PUBLICATIONES MATHEMATICAE DEBRECEN, 2013, 83 (03) :359-374

[4] Global and exploding solutions for nonlocal quadratic evolution problems [J].

Biler, P ;

Woyczynski, WA .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1998, 59 (03) :845-869

[5] Blowup of solutions to generalized Keller-Segel model [J].

Biler, Piotr ;

Karch, Grzegorz .

JOURNAL OF EVOLUTION EQUATIONS, 2010, 10 (02) :247-262

[6]

Blanchet A, 2006, ELECTRON J DIFFER EQ

[7] The one-dimensional Keller-Segel model with fractional diffusion of cells [J].

Bournaveas, Nikolaos ;

Calvez, Vincent .

NONLINEARITY, 2010, 23 (04) :923-935

[8] Diffusion, attraction and collapse [J].

Brenner, MP ;

Constantin, P ;

Kadanoff, LP ;

Schenkel, A ;

Venkataramani, SC .

NONLINEARITY, 1999, 12 (04) :1071-1098

[9] Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation [J].

Burczak, Jan ;

Granero-Belinchon, Rafael .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (09) :6115-6142

[10]

Caldern AP., 1954, Stud. Math, V14, P249, DOI [DOI 10.4064/SM-14-2-249-271, 10.4064/sm-14-2-249-271]

← 1 2 3 4 →