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Almqvist, A., Burtseva, E., Ràfols, F. P. & Wall, P. (2019). New insights on lubrication theory for compressible fluids. International Journal of Engineering Science, 145, Article ID 103170.
Open this publication in new window or tab >>New insights on lubrication theory for compressible fluids
2019 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, article id 103170Article in journal (Refereed) Published
Abstract [en]

The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Thin film approximation, Reynold’s equation, Compressible flow, Navier–Stokes equations, Dimension reduction, Asymptotic analysis
National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
Research subject
Machine Elements; Mathematics
Identifiers
urn:nbn:se:ltu:diva-76138 (URN)10.1016/j.ijengsci.2019.103170 (DOI)000496842000009 ()2-s2.0-85072601607 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-09-27 (johcin)

Available from: 2019-09-27 Created: 2019-09-27 Last updated: 2019-12-09Bibliographically approved
Burtseva, E., Lundberg, S., Persson, L.-E. & Samko, N. (2018). Multi–dimensional Hardy type inequalities in Hölder spaces. Journal of Mathematical Inequalities, 12(3), 719-729
Open this publication in new window or tab >>Multi–dimensional Hardy type inequalities in Hölder spaces
2018 (English)In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 719-729Article in journal (Refereed) Published
Abstract [en]

Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

Place, publisher, year, edition, pages
Zagreb: Element, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69692 (URN)10.7153/jmi-2018-12-55 (DOI)000445366500010 ()
Note

Validerad;2018;Nivå 2;2018-06-26 (andbra)

Available from: 2018-06-19 Created: 2018-06-19 Last updated: 2018-10-15Bibliographically approved
Burtseva, E., Persson, L.-E. & Samko, N. (2018). Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces. Mathematische Nachrichten, 291(11-12), 1655-1665
Open this publication in new window or tab >>Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces
2018 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 11-12, p. 1655-1665Article in journal (Refereed) Published
Abstract [en]

We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).

Place, publisher, year, edition, pages
John Wiley & Sons, 2018
Keywords
boundedness, compactification, Hardy‐type inequalities, Hardy‐type operators, Hölder spaces, spherical means, weighted estimates, Primary: 26D15, 46E15, Secondary: 47B38
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-68198 (URN)10.1002/mana.201700356 (DOI)000441003600002 ()2-s2.0-85051175788 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-08-09 (andbra)

Available from: 2018-04-05 Created: 2018-04-05 Last updated: 2019-09-13Bibliographically approved
Burtseva, E. & Samko, N. (2017). On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces. Fractional Calculus and Applied Analysis, 20(6), 1545-1566
Open this publication in new window or tab >>On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces
2017 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 20, no 6, p. 1545-1566Article in journal (Refereed) Published
Abstract [en]

We study weighted generalized Hardy and fractional operators acting from generalized Morrey spaces Lp,φ,(n) into Orlicz-Morrey spaces LΦ,φ,(n). We deal with radial quasi-monotone weights and assumptions imposed on weights are given in terms of Zigmund-type integral conditions. We find conditions on φ,Φ, the weight w and the kernel of the fractional operator, which insures such a boundedness. We prove some pointwise estimates for weighted generalized fractional operators via generalized Hardy operators, which allow to obtain the weighted boundedness for fractional operators from those for Hardy operators. We provide also some easy to check numerical inequalities to verify the obtained conditions.

Place, publisher, year, edition, pages
Walter de Gruyter, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-67715 (URN)10.1515/fca-2017-0081 (DOI)000424675400013 ()2-s2.0-85041948540 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-02-21 (andbra)

Available from: 2018-02-21 Created: 2018-02-21 Last updated: 2019-04-23Bibliographically approved
Burtseva, E., Lundberg, S., Persson, L.-E. & Samko, N. (2017). Potential type operators in PDEs and their applications. Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4-8 July 2016. AIP Conference Proceedings, 1798, Article ID 020178.
Open this publication in new window or tab >>Potential type operators in PDEs and their applications
2017 (English)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020178Article in journal (Refereed) Published
Abstract [en]

 We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

Place, publisher, year, edition, pages
AIP Publishing, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-62316 (URN)10.1063/1.4972770 (DOI)000399203000177 ()2-s2.0-85013628861 (Scopus ID)
Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4-8 July 2016
Note

2017-03-03 (andbra);Konferensartikel i tidskrift

Available from: 2017-03-06 Created: 2017-03-06 Last updated: 2018-11-20Bibliographically approved
Burtseva, E. (2017). Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane. Mediterranean Journal of Mathematics, 14(5), Article ID 203.
Open this publication in new window or tab >>Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane
2017 (English)In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 14, no 5, article id 203Article in journal (Refereed) Published
Abstract [en]

We study the boundedness of the Cauchy singular integral operators on curves in complex plane in generalized Morrey spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of singular integral operators in weighted generalized Morrey spaces.

Place, publisher, year, edition, pages
Birkhauser Verlag, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-65603 (URN)10.1007/s00009-017-1004-9 (DOI)000411133500021 ()2-s2.0-85029601443 (Scopus ID)
Note

Validerad;2017;Nivå 2;2017-09-12 (andbra)

Available from: 2017-09-12 Created: 2017-09-12 Last updated: 2018-06-15Bibliographically approved
Burtseva, E. (2016). Operators and Inequalities in various Function Spaces and their Applications. (Licentiate dissertation). Luleå: Luleå University of Technology
Open this publication in new window or tab >>Operators and Inequalities in various Function Spaces and their Applications
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate thesis is devoted to the study of mapping properties of different operators (Hardy type, singular and potential) between various function spaces.

The main body of the thesis consists of five papers and an introduction, which puts these papers into a more general frame.

In paper A we prove the boundedness of the Riesz Fractional Integration Operator from a Generalized Morrey Space to a certain Orlicz-Morrey Space, which covers the Adams resultfor Morrey Spaces. We also give a generalization to the case of Weighted Riesz Fractional Integration Operators for a class of weights.

In paper B we study the boundedness of the Cauchy Singular Integral Operator on curves in complex plane in Generalized Morrey Spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of Singular Integral Operators in Weighted Generalized Morrey Spaces.

In paper C we prove the boundedness of the Potential Operator in Weighted Generalized Morrey Spaces in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation with a free term in such a space. We also give a short overview of some typical situations when Potential type Operators arise when solving PDEs.

​In paper D some new inequalities of Hardy type are proved. More exactly, the boundedness of multidimensional Weighted Hardy Operators in Hölder Spaces are proved in cases with and without compactification.

In paper E the mapping properties are studied for Hardy type and Generalized Potential type Operators in Weighted Morrey type Spaces.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2016
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-59666 (URN)978-91-7583-723-9 (ISBN)978-91-7583-724-6 (ISBN)
Presentation
2016-12-14, E246, Luleå University of Technology, Luleå, 15:00 (English)
Opponent
Supervisors
Available from: 2016-10-13 Created: 2016-10-11 Last updated: 2018-06-15Bibliographically approved
Burtseva, E. & Samko, N. (2016). Weighted Adams type theorem for the Riesz fractional integral in generalized Morrey Space. Fractional Calculus and Applied Analysis, 19(4), 954-972
Open this publication in new window or tab >>Weighted Adams type theorem for the Riesz fractional integral in generalized Morrey Space
2016 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 19, no 4, p. 954-972Article in journal (Refereed) Published
Abstract [en]

We prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space L-p,L-phi to a certain Orlicz-Morrey space L-Phi,L-phi which covers the Adams result for Morrey spaces. We also give a generalization to the case of weighted Riesz fractional integration operators for some class of weights.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-59748 (URN)10.1515/fca-2016-0052 (DOI)000383390700014 ()2-s2.0-84985023407 (Scopus ID)
Note

Validerad; 2016; Nivå 2; 2016-10-14 (andbra)

Available from: 2016-10-14 Created: 2016-10-14 Last updated: 2018-10-04Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1963-6829

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