# Solvability of the Navier-Stokes System with L{sup 2} Boundary Data

## Abstract

We prove the existence of the very weak solution of the Dirichlet problem for the Navier-Stokes system with L{sup 2} boundary data. Under the small data assumption we also prove the uniqueness. We use the penalization method to study the linearized problem and then apply Banach's fixed point theorem for the nonlinear problem with small boundary data. We extend our result to the case with no small data assumption by splitting the data on a large regular and small irregular part.

- Authors:

- Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb (Croatia)

- Publication Date:

- OSTI Identifier:
- 21064272

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 41; Journal Issue: 3; Other Information: DOI: 10.1007/s002459911018; Copyright (c) 2000 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 2000 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; MATHEMATICAL SOLUTIONS; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS

### Citation Formats

```
Marusic-Paloka, E.
```*Solvability of the Navier-Stokes System with L{sup 2} Boundary Data*. United States: N. p., 2000.
Web. doi:10.1007/S002459911018.

```
Marusic-Paloka, E.
```*Solvability of the Navier-Stokes System with L{sup 2} Boundary Data*. United States. doi:10.1007/S002459911018.

```
Marusic-Paloka, E. Mon .
"Solvability of the Navier-Stokes System with L{sup 2} Boundary Data". United States. doi:10.1007/S002459911018.
```

```
@article{osti_21064272,
```

title = {Solvability of the Navier-Stokes System with L{sup 2} Boundary Data},

author = {Marusic-Paloka, E.},

abstractNote = {We prove the existence of the very weak solution of the Dirichlet problem for the Navier-Stokes system with L{sup 2} boundary data. Under the small data assumption we also prove the uniqueness. We use the penalization method to study the linearized problem and then apply Banach's fixed point theorem for the nonlinear problem with small boundary data. We extend our result to the case with no small data assumption by splitting the data on a large regular and small irregular part.},

doi = {10.1007/S002459911018},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 3,

volume = 41,

place = {United States},

year = {2000},

month = {5}

}

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