Skip to main content

Integrability and the Properties of Solutions to Euler and Navier-Stokes Equations | Chapter 07 | Theory and Applications of Mathematical Science Vol. 2


It is known that the Euler and Navier-Stokes equations, which describe flows of ideal and viscid gases, are the set of equations of the conservation laws for energy, linear momentum and mass. As it will be shown, the integrability and properties of the solutions to the Euler and Navier-Stokes equations depend, firstly, on the consistency of equations of the conservation laws and, secondly, on the properties of conservation laws.

It was found that the Euler and Navier-Stokes equations have solutions of  two types, namely, the solutions that are not functions (depend not only on coordinates) and generalized solutions that are functions but realized discretely and hence, functions or their derivatives have discontinuities. A transition from the solutions of first type to generalized solutions describes the process of transition of gas-dynamic medium from non-equilibrium state to the locally-equilibrium one. Such a process is accompanied by the emergence of any observable formations (such as waves, vortices, turbulent pulsations and soon). This discloses the mechanism of such processes as emergence vorticity and turbulence.

Such results were obtained when studying the equations the conservation laws for energy and linear momentum, which turned out to be inconsistent, due to the non-commutativity of the conservation laws.

Author(s) Details

L. I. Petrova
Moscow State University, Russia.


Comments

Popular posts from this blog

A Prospective Study about Safety and Efficacy of Perioperative Lidocaine Infusion | Chapter 09 | New Horizons in Medicine and Medical Research Vol. 8

 Opioids cause clinically significant side effects such as respiratory depression, immunosuppression, muscle rigidity, negative inotropism, nausea, vomiting, hyperalgesia, urine retention, postoperative ileus, and drowsiness. Perioperative opioids are a major contributor to the United States' and other countries' opioid epidemics. Non-opioid analgesics, particularly lidocaine, are becoming more common for perioperative use as a result of this. A total of 185 adult patients were randomly assigned to one of two groups: control group I (105 patients) [fentanyl group] or group ii (80 patients) [opioid-free anaesthesia group]. Lidocaine 1.5 mg/kg bolus followed by 1.5 mg/kg/h infusion intraoperatively, and 1.5-2 mg/kg/h infusion for 2-8 hours postoperatively were given to patients in both groups at anaesthetic induction. Intraoperatively, both groups received analgesic adjuvants such as diclofenac 75 mg, paracetamol 1 gm, and mgso4 30-50 mg/kg. If the mean arterial pressure (map)

A Brief Study of Middleware Technologies: Programming Applications and Management Systems | Chapter 15 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

  Many platforms, services, applications, hardware, and operating systems are connected through the middleware layer. Because the middleware layer abstracts much low-level complexity and makes applications and software systems portable, it allows disparate systems to interface and function together in harmony. Middleware technologies enable software engineers to swiftly construct software systems and applications, allowing developers to focus on more important tasks. This chapter examines several types of middleware systems and discusses middleware capabilities, middleware operation, middleware's function in cloud-based systems, and the best middleware platforms to use. Middleware systems are widely utilised and can be found in practically any software system or application. Middleware programmes provide as a link between many sorts of systems and protocols. They serve as a mechanism for various systems. To successfully exchange information, it runs on a variety of operating system

Ethnopharmacological Survey among Traditional Medicine Practitioners in Abidjan (Côte d'Ivoire) for the Management of Pathologies such as Malaria, ENT Diseases, Diarrhea, Typhoid Fever and Anemia | Chapter 05 | New Horizons in Medicine and Medical Research Vol. 8

 Traditional Medicine Practitioners (TMPs) of Côte d'Ivoire are familiar with the therapeutic herbs. Medicinal plants have been shown to be useful in the treatment of common diseases such as malaria (KROA, 2004) and diabetes (N'GUESSAN et al, 2013) in several studies and scientific study. In the Abidjan District, the current policy is to integrate traditional medicine and pharmacopoeia into the national health system in order to improve population health coverage, particularly in the management of commonly encountered diseases such as malaria, ENT diseases, diarrhoea, typhoid fever, and anaemia. This research aims to increase the use of traditional medicine and pharmacopoeia in the national health system. Over the course of three months, fifty (50) PMTs in the District of Abidjan participated in this study. Plant therapists accounted for 30 of the 50 PMTs polled at the end of the study, or 60%. Traditional medicine centres use 61 types of medicinal plants from 36 famili