By G.P. Galdi (auth.)

The booklet presents a accomplished, targeted and self-contained therapy of the basic mathematical homes of boundary-value difficulties regarding the Navier-Stokes equations. those homes comprise lifestyles, specialty and regularity of ideas in bounded in addition to unbounded domain names. each time the area is unbounded, the asymptotic habit of suggestions can be investigated.

This booklet is the hot version of the unique quantity ebook, less than an analogous identify, released in 1994.

In this re-creation, the 2 volumes have merged into one and extra chapters on regular generalized oseen move in external domain names and regular Navier–Stokes stream in three-d external domain names were extra. lots of the proofs given within the earlier version have been additionally updated.

An introductory first bankruptcy describes all appropriate questions taken care of within the ebook and lists and motivates a couple of major and nonetheless open questions. it's written in an expository type for you to be obtainable additionally to non-specialists. each one bankruptcy is preceded by means of a considerable, initial dialogue of the issues handled, besides their motivation and the tactic used to resolve them. additionally, each one bankruptcy ends with a piece devoted to replacement ways and approaches, in addition to ancient notes.

The booklet includes greater than four hundred stimulating workouts, at varied degrees of hassle, that might support the junior researcher and the graduate scholar to steadily develop into accustomed with the topic. eventually, the publication is endowed with an enormous bibliography that comes with greater than 500 goods. each one merchandise brings a connection with the component to the ebook the place it truly is brought up.

The e-book might be beneficial to researchers and graduate scholars in arithmetic specifically mathematical fluid mechanics and differential equations.

Review of First version, First Volume:

“The emphasis of this e-book is on an advent to the mathematical conception of the desk bound Navier-Stokes equations. it's written within the variety of a textbook and is basically self-contained. the issues are offered basically and in an available demeanour. each bankruptcy starts off with an excellent introductory dialogue of the issues thought of, and ends with fascinating notes on assorted techniques built within the literature. extra, stimulating routines are proposed. (Mathematical experiences, 1995)

**Read or Download An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems PDF**

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**Extra resources for An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems **

**Sample text**

Similar questions can be formulated for regions having “outlets” to infinity whose cross sections are not necessarily bounded. 1) (with v ∗ = 0) under the condition of prescribed flux and vanishing velocity as |x| tends to infinity in each “outlet” Ωi . Unlike flow in exterior regions, here the case of two-dimensional solutions presents results more complete than in the case of fully three-dimensional motions, thanks to the thorough investigation of Amick and Fraenkel (1980). ” However, two important issues are left out, that is, uniqueness of solutions and their order of decay at large distances.

However, unlike the results of Ladyzhenskaya and Solonnikov, the results of all the preceding authors require that the flux Φ be sufficiently small. Therefore, we have the following question: (iv) Is it possible to show the known results for three-dimensional flow in the aperture domain for an arbitrary flux Φ? It should be remarked that the two-dimensional analogue of this problem appears to be difficult to treat, and all methods employed by the above authors 28 Of course, we may assume that one section verifies (a) and the other verifies (b).

Similar questions can be formulated for regions having “outlets” to infinity whose cross sections are not necessarily bounded. 1) (with v ∗ = 0) under the condition of prescribed flux and vanishing velocity as |x| tends to infinity in each “outlet” Ωi . Unlike flow in exterior regions, here the case of two-dimensional solutions presents results more complete than in the case of fully three-dimensional motions, thanks to the thorough investigation of Amick and Fraenkel (1980). ” However, two important issues are left out, that is, uniqueness of solutions and their order of decay at large distances.