Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains*

被引：6

作者：

Casas, Eduardo ^{[1
]}

Kunisch, Karl ^{[2
]}

机构：

[1] Univ Cantabria, ETSI Ind & Telecomunicac, Dept Matemat Aplicada & Ciencias Comp, Santander 39005, Spain

[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2021年 / 27卷

基金：

欧盟地平线“2020”;

关键词：

Evolution Navier-Stokes equations; weak solutions; uniqueness clasess; sensitivity analysis; asymptotic stability;

D O I：

10.1051/cocv/2021058

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Existence and uniqueness of solutions to the Navier-Stokes equations in dimension two with forces in the space L-q((0, T); W--1,W-p(omega)) for p and q in appropriate parameter ranges are proven. The case of spatially measured-valued forces is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions for any 1 < p, q < infinity.

引用

页数：25

共 31 条

[1]

Amann H., 2001, REAL ACAD CIENCIAS E, V95, P85

[2]

Amann H., 1995, Monographs in Mathematics, VI

[3] ON THE EXISTENCE AND REGULARITY OF THE SOLUTION OF STOKES PROBLEM IN ARBITRARY DIMENSION [J].

AMROUCHE, C ;

GIRAULT, V .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1991, 67 (05) :171-175

[4] The square root problem for second-order, divergence form operators with mixed boundary conditions on L p [J].

Auscher, Pascal ;

Badr, Nadine ;

Haller-Dintelmann, Robert ;

Rehberg, Joachim .

JOURNAL OF EVOLUTION EQUATIONS, 2015, 15 (01) :165-208

[5] A Mathematical Model for the Industrial Hazardous Waste Location-Routing Problem [J].

Boyer, Omid ;

Hong, Tang Sai ;

Pedram, Ali ;

Yusuff, Rosnah Bt Mohd ;

Zulkifli, Norzima .

JOURNAL OF APPLIED MATHEMATICS, 2013,

[6]

Brezis H, 2011, UNIVERSITEXT, P1

[7] OPTIMAL CONTROL OF THE TWO-DIMENSIONAL STATIONARY NAVIER-STOKES EQUATIONS WITH MEASURE VALUED CONTROLS [J].

Casas, Eduardo ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2019, 57 (02) :1328-1354

[8]

Cattabriga Lamberto, 1961, REND SEMIN MAT U PAD, V31, P308

[9] On maximal parabolic regularity for non-autonomous parabolic operators [J].

Disser, Karoline ;

ter Elst, A. F. M. ;

Rehberg, Joachim .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (03) :2039-2072

[10] Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bounded domains of R2 [J].

Farwig, R. ;

Galdi, G. P. ;

Sohr, H. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (02) :564-580

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