| Articolul precedent |
| Articolul urmator |
 |
 223 1 |
| Ultima descărcare din IBN: 2021-09-30 12:42 |
 SM ISO690:2012BALTAG, Iurie. Determination on some solutions to the stationary 2D Navier-Stokes equation. In: Mathematics and Information Technologies: Research and Education, Ed. 2021, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, p. 14. |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
| Mathematics and Information Technologies: Research and Education 2021 | ||||||
|
Conferința "Mathematics and Information Technologies: Research and Education" 2021, Chişinău, Moldova, 1-3 iulie 2021 | ||||||
|
||||||
| Pag. 14-14 | ||||||
|
||||||
 Descarcă PDF |
||||||
| Rezumat | ||||||
Consider the following system of partial differential equations: 8>< >: Px ¹ + uux + vuy = a(uxx + uyy) + Fx Py ¹ + uvx + vvy = a(vxx + vyy) + Fy ux + vy = 0 (1) P = P(x; y); u = u(x; y); v = v(x; y); x; y 2 R; where P; u; v; F : D ! R2. The system (1) describes the process of stationary fluid flow or gas on a flat surface. The function P represents the pressure of the liquid, and functions u; v represent the flow of the liquid (gas). The constants a > 0 and ¹ > 0 are determined by the parameters of the liquids (of the gas), which are viscosity and liquid’s density. The function F represents the exterior forces. Theorem. Suppose that u; v 2 C2(D) admit the bounded derivatives up to including order 2 in D. If f(z), z = x + iy, is an analytical function in D, then (u; v; P), with u = Imf, v = Ref, P = [F ¡0; 5(u2+v2)+c]¹ are solutions to the system (1). If W(x; y) is a harmonic function in D, then (u; v; P), with u = Wy + c1y + c2; v = ¡Wx + c3x + c4; P = [F ¡ 0; 5(u2 + v2) + (c1 ¡ c3)W + 0; 5(c1y2 ¡ c3x2) + c2y ¡ c4x + c]¹; and the arbitrary constants c; c1; c2; c3; c4 are solutions to the system (1). In addition, various special cases were studied, and particular and exact solutions of the system (1) were found in these cases. |
||||||
|
Cerif XML Export
<?xml version='1.0' encoding='utf-8'?> <CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'> <cfResPubl> <cfResPublId>ibn-ResPubl-134071</cfResPublId> <cfResPublDate>2021</cfResPublDate> <cfStartPage>14</cfStartPage> <cfISBN></cfISBN> <cfURI>https://ibn.idsi.md/ro/vizualizare_articol/134071</cfURI> <cfTitle cfLangCode='EN' cfTrans='o'>Determination on some solutions to the stationary 2D Navier-Stokes equation</cfTitle> <cfAbstr cfLangCode='EN' cfTrans='o'><p>Consider the following system of partial differential equations: 8>< >: Px ¹ + uux + vuy = a(uxx + uyy) + Fx Py ¹ + uvx + vvy = a(vxx + vyy) + Fy ux + vy = 0 (1) P = P(x; y); u = u(x; y); v = v(x; y); x; y 2 R; where P; u; v; F : D ! R2. The system (1) describes the process of stationary fluid flow or gas on a flat surface. The function P represents the pressure of the liquid, and functions u; v represent the flow of the liquid (gas). The constants a > 0 and ¹ > 0 are determined by the parameters of the liquids (of the gas), which are viscosity and liquid’s density. The function F represents the exterior forces. Theorem. Suppose that u; v 2 C2(D) admit the bounded derivatives up to including order 2 in D. If f(z), z = x + iy, is an analytical function in D, then (u; v; P), with u = Imf, v = Ref, P = [F ¡0; 5(u2+v2)+c]¹ are solutions to the system (1). If W(x; y) is a harmonic function in D, then (u; v; P), with u = Wy + c1y + c2; v = ¡Wx + c3x + c4; P = [F ¡ 0; 5(u2 + v2) + (c1 ¡ c3)W + 0; 5(c1y2 ¡ c3x2) + c2y ¡ c4x + c]¹; and the arbitrary constants c; c1; c2; c3; c4 are solutions to the system (1). In addition, various special cases were studied, and particular and exact solutions of the system (1) were found in these cases.</p></cfAbstr> <cfResPubl_Class> <cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId> <cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId> <cfStartDate>2021T24:00:00</cfStartDate> </cfResPubl_Class> <cfResPubl_Class> <cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId> <cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId> <cfStartDate>2021T24:00:00</cfStartDate> </cfResPubl_Class> <cfPers_ResPubl> <cfPersId>ibn-person-689</cfPersId> <cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId> <cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId> <cfStartDate>2021T24:00:00</cfStartDate> </cfPers_ResPubl> </cfResPubl> <cfPers> <cfPersId>ibn-Pers-689</cfPersId> <cfPersName_Pers> <cfPersNameId>ibn-PersName-689-3</cfPersNameId> <cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId> <cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId> <cfStartDate>2021T24:00:00</cfStartDate> <cfFamilyNames>Baltag</cfFamilyNames> <cfFirstNames>Iurie</cfFirstNames> </cfPersName_Pers> </cfPers> </CERIF>
|
|
|
