How Long to Read Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations

How Long Does it Take to Read Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations?

It takes the average reader 9 hours and 12 minutes to read Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by Jared Speck

Assuming a reading speed of 250 words per minute. Learn more

Description

In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-data solutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics, hyperbolic conservation laws, wave equations, and geometric analysis.

How long is Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations?

Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by Jared Speck is 544 pages long, and a total of 138,176 words.

This makes it 184% the length of the average book. It also has 169% more words than the average book.

How Long Does it Take to Read Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 12 hours and 35 minutes to read Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations aloud.

What Reading Level is Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations?

Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations?

Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by Jared Speck is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

To buy Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by Jared Speck on Amazon click the button below.