non conservative form of navier stokes equations

... http://www.boundaryvalueproblems.com/content/2011/1/43 Page 19 of 19 References Hoff, D, Serre, D: The failure of continuous dependence on initial data for the Navier- Stokes equations of compressible flow SIMA J Appl Math ... 0 ≤ C2 (T) The proof is complete Proof of Theorem 3.1 By Lemmas 3.2-3.3, Theorem 2.1 and Sobolev’s embedding theorem, we complete the proof of Theorem 3.1 Global existence of solutions in H4 ... dxds x which, by virtue of Gronwall’s inequality, (2.1) and (2.14), gives (2.19) Proof of Theorem 2.1 By Lemmas 2.1-2.3, we complete the proof of Theorem 2.1 Global existence of solutions in H2 For...

Ngày tải lên: 20/06/2014, 22:20

... = Z0 and therefore completes the proof of Proposition 4.4 1011 ERGODICITY OF THE 2D NAVIER- STOKES EQUATIONS 4.2 Malliavin calculus and the Navier- Stokes equations In this section, we give a ... under the nonlinearity of the 2D Navier- Stokes equations (i.e they are preserved by the flow of (1.1) if ν = and ξ = 0) 994 MARTIN HAIRER AND JONATHAN C MATTINGLY From a careful study of the nonlinearity ... ergodicity of the two dimensional Navier- Stokes equations To so, we employ information on the structure of the nonlinearity from [EM01] which was developed there to prove ergodicity of the finite...

Ngày tải lên: 29/03/2014, 07:20

... regularity of the pressure of weak solutions of Navier- Stokes equations, ” Archiv der Mathematik, vol 46, no 5, pp 428–439, 1986 L Iskauriaza, G A Ser¨ gin, and V Shverak, “L3,∞ -solutions of Navier- Stokes ... Navier- Stokes equations in terms of the pressure,” Journal of Differential Equations, vol 244, no 11, pp 2963–2979, 2008 14 Y Zhou, “On regularity criteria in terms of pressure for the Navier- Stokes ... regularity of weak solutions of the Navier- Stokes equations, ” Archive for Rational Mechanics and Analysis, vol 9, no 1, pp 187–195, 1962 T Ohyama, “Interior regularity of weak solutions of the time-dependent...

Ngày tải lên: 22/06/2014, 02:20

... studies on nonlinear stability of the solutions of the high dimensional compressible Navier- Stokes equations in the whole space Rn However, with the presence of boundary conditions, all of the above ... Dirichlet data In view of results of above studies, to find precise pointwise structure of Green’s function of initial boundary problem of linearized compressible Navier- Stokes equations around constant ... progresses in the research of the pointwise structure of the fundamental solution in one dimensional Navier- Stokes equations are shown, which lead to results on nonlinear stability of the solution in...

Ngày tải lên: 10/09/2015, 09:06

... nonisentropic and compressible Euler equations The aim of this paper is to justify rigorously the local existence of smooth solutions of system 1.1 and the convergence of system 1.1 to this formal ... 4.2 Proof of Convergence Obviously, the existence and uniqueness of smooth solutions of 2.3 are equivalent to that of 4.6 or 4.9 Then, in order to rigorously justify the convergence of 2.3 to ... the existence of smooth solutions to the problem 1.1 and their convergence to the solutions of the compressible and nonisentropic Euler equations in a time interval independent of For this propose,...

Ngày tải lên: 21/06/2014, 11:20

... Method for the (2D) Incompressible Navier- Stokes Equations Master of Science Thesis Chair of Aerodynamics Department of Aerospace Engineering Delft University of Technology January 2006 by Reinout ... numerical study and the construction of a 2D IBMs code for the steady Navier- Stokes equations, including grid generator These three parts form the main structure of this report The fourth and last ... points The construction of a steady 2D Navier- Stokes code provided an opportunity to test some of the findings from the 1D numerical study in a higher dimension A lot of effort was put in constructing...

Ngày tải lên: 11/07/2014, 23:20

... Navier- Stokes- Voight equations as an inviscid regularization of the 3D incompressible Navier- Stokes equations, and further obtained the existence of global attractors for Navier- Stokes- Voight equations ... models for the 3D Navier- Stokes- Voight equations Chin Ann Math 30(B), 697–714 (2009) Qin, Y, Yang, X, Xin, Liu: Uniform attractors for a 3D non- autonomous Navier- Stokes- Voight Equations, Preprint ... property of the functional 〈·,·〉 + a2 〈∇·, ∇·〉, the conclusion holds □ Proof of Theorem 2.3 From Lemmas 3.1-3.3, we can deduce the result easily □ Proof of Theorem 2.4 Similarly to the proof of Theorem...

Ngày tải lên: 20/06/2014, 21:20

... Navier- Stokes- Voight equations as an inviscid regularization of the 3D incompressible Navier- Stokes equations, and further obtained the existence of global attractors for Navier- Stokes- Voight equations ... models for the 3D Navier- Stokes- Voight equations Chin Ann Math 30(B), 697–714 (2009) Qin, Y, Yang, X, Xin, Liu: Uniform attractors for a 3D non- autonomous Navier- Stokes- Voight Equations, Preprint ... property of the functional 〈·,·〉 + a2 〈∇·, ∇·〉, the conclusion holds □ Proof of Theorem 2.3 From Lemmas 3.1-3.3, we can deduce the result easily □ Proof of Theorem 2.4 Similarly to the proof of Theorem...

Ngày tải lên: 20/06/2014, 22:20

... give the information of one candidate‟s performance in relation to that of other candidates With the result of this kind of tests, we are not told directly how well the candidate has performed in ... favour End -of- semester tests, which are of concern to the author of this thesis, 35 and end -of- year tests are required to be designed in the form of MCQs and to follow the construction of tests ... 20%, consists of items for each form The total number of items of the test is 50 which is expected to be completed in 60 minutes The current testing situation There are two forms of assessment...

Ngày tải lên: 28/03/2015, 10:05

... result, the study of the Navier- Stokes equations becomes one of the most popular areas of modern mathematics In this thesis, We will focus on the one dimensional Navier- Stokes equations and consider ... nonlinear problem Chapter Introduction The study of Navier- Stokes equations is an important area in fluid mechanics The interest of studying Navier- Stokes equations rises from both practically and academically ... because the variables of these equations have different meaning The variables of the Navier- Stokes equations are thermodynamical parameters while the variables of the Boltzmann equations or the Broadwell...

Ngày tải lên: 09/09/2015, 10:15

... UNIVERSITY, HANOI UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES DEPARTMENT OF POST-GRADUATE STUDIES  NGUYỄN VĂN A M.A MINOR THESIS SYNTACTIC AND SEMANTICO - PRAGMATIC FEATURES OF YES-NO QUESTIONS ... UNIVERSITY, HANOI UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES DEPARTMENT OF POST-GRADUATE STUDIES  NGUYỄN VĂN A M.A MINOR THESIS SYNTACTIC AND SEMANTICO-PRAGMATIC FEATURES OF YES-NO QUESTIONS ... UNIVERSITY, HANOI UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES DEPARTMENT OF POST-GRADUATE STUDIES  NGUYỄN VĂN A M.A MINOR THESIS SYNTACTIC AND SEMANTICO-PRAGMATIC FEATURES OF YES-NO QUESTIONS...

Ngày tải lên: 07/11/2012, 15:07

... (including tone of voice, inflection and other sounds) and 55 percent nonverbal (Pease, 1984:6) Importance of nonverbal communication - Mehrabian 7% Verbal Nonverbal 93% Chart 1: Importance of Nonverbal ... influence of some of informants’ parameters on the way they “decode” the nonverbal cues of their communicating partners 3.1.3.1 Length of stay or work with native people American informants have ... expressiveness as seen from informants' length of stay The table shows the influence of the informants’ length of stay or work with native people on their perception of the amount of expressiveness The...

Ngày tải lên: 07/11/2012, 15:07

... inspected American nonverbal expressions of disappointment through Vietnamese informants’ perception and Vietnamese nonverbal ways of expressing disappointment through American informants’ observation ... Table 4: Amount of expressiveness as seen from informants' length of stay Table 5: Amount of expressiveness as seen from the informants' cultural knowledge Table 6: Influence of communicating ... Chart 1: Importance of Nonverbal Communication Diagram 1: Classification of Nonverbal Communication Chart 2: Amount of expressiveness in American and Vietnamese cultures vi TABLE OF CONTENTS PART...

Ngày tải lên: 07/11/2012, 15:07

... problem extremely (difficulty) 81.I’d like some (inform) about your school, please 82.Waching TV has become one of the most populat forms of (entertain) 83.Nowaday, internet is (commerce) used ... mgazine (inform) It’s full of rubbish 90.Rading newspapers every day is an effective means of keeping up with the (late) and (globe) 91 W website is a place where you can createand read (inform) on ... thought (height) of her ways of reducing the amount of garbage 133 The food in the restaurant was (wonder) delicious, but the service was (awful) poor 134 He got an electric shock because of his (care)...

Ngày tải lên: 20/09/2013, 12:10

... odeint are drivers Section 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equations (Chapter 19) Sample ... description of each of these types follows Runge-Kutta methods propagate a solution over an interval by combining the information from several Euler-style steps (each involving one evaluation of the ... basic formulas of the method, starts with dependent variables yi at x, and calculates new values of the dependent variables at the value x + h The algorithm routine also yields up some information...

Ngày tải lên: 15/12/2013, 04:15

... be monitored Implementation of adaptive stepsize control requires that the stepping algorithm signal information about its performance, most important, an estimate of its truncation error In this ... is the routine for carrying out one classical Runge-Kutta step on a set of n differential equations You input the values of the independent variables, and you get out new values which are stepped ... step in a sequence of steps in identical manner Prior behavior of a solution is not used in its propagation This is mathematically proper, since any point along the trajectory of an ordinary differential...

Ngày tải lên: 15/12/2013, 04:15

... set of equations to be solved can be written as the N ×N set of equations (AT · A) · x = (AT · b) (2.0.4) where AT denotes the transpose of the matrix A Equations (2.0.4) are called the normal equations ... corresponding x’s are then the columns of the matrix inverse of A (§2.1 and §2.3) • Calculation of the determinant of a square matrix A (§2.3) If M < N , or if M = N but the equations are degenerate, then ... combination of (typically) N − M vectors (which are said to be in the nullspace of the matrix A) The task of finding the solution space of A involves • Singular value decomposition of a matrix...

Ngày tải lên: 15/12/2013, 04:15

... two rows of A and the corresponding rows of the b’s and of 1, does not change (or scramble in any way) the solution x’s and Y Rather, it just corresponds to writing the same set of linear equations ... combination of itself and any other row, as long as we the same linear combination of the rows of the b’s and (which then is no longer the identity matrix, of course) • Interchanging any two columns of ... as the pivot is a very good choice A curiosity of this procedure, however, is that the choice of pivot will depend on the original scaling of the equations If we take the third linear equation...

Ngày tải lên: 15/12/2013, 04:15

... Instead of doing O(N ) operations each time to solve the equations from scratch, one can often update a matrix factorization in O(N ) operations and use the new factorization to solve the next set of ... one can write formulas for the c’s that involve only seven multiplications? (Try it yourself, before reading on.) Such a set of formulas was, in fact, discovered by Strassen [1] The formulas are: ... applications only the part (2.10.4) of the algorithm is needed, so we separate it off into its own routine rsolv Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)...

Ngày tải lên: 15/12/2013, 04:15