How Long to Read Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle

How Long Does it Take to Read Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle?

It takes the average reader 4 hours and 38 minutes to read Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle by Massimiliano Berti

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

Description

The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.

How long is Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle?

Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle by Massimiliano Berti is 269 pages long, and a total of 69,671 words.

This makes it 91% the length of the average book. It also has 85% more words than the average book.

How Long Does it Take to Read Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle Aloud?

The average oral reading speed is 183 words per minute. This means it takes 6 hours and 20 minutes to read Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle aloud.

What Reading Level is Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle?

Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle 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 Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle?

Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle by Massimiliano Berti is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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